Someone gave me a laptop with 2.2 GHz, 64bit, 8 Gb Ram, and integrated graphics. I'm probably going to put Ubuntu on it and put some games on it, but obviously they are going to be in the older end of my library. About what year should I look for for games that would run on these specs? I did not game in between the 80s and the 2010s, so I have no clue. Thanks!

I'd suggest Fedora over Ubuntu, but that's mostly for the sake of having access to modern packages and not having to swim uphill against backports or play with fire/PPAs.

As to what games, depends. You planning to use Wine?

If able, would you please indicate which CPU you are using?
If unknown, would you kindly share the model of the gifted laptop?

In the past, on one of my oldest computers (1.8 Ghz Intel Core 2 Duo) with horribly underpowered integrated graphics, I had been able to play quite a few games requiring graphics acceleration (native Linux and Wine).

It's an Intel(R) Core i3-2330M. hp laptop of some description That's surprisingly late!

It includes 'Intel HD 3000' integrated graphics. While obviously not great, you should be able to run quite a few less demanding games. I had been able to play the turn-based Xenonauts (2014) on the aforementioned much weaker CPU (with Graphics Media Accelerator integrated graphics).

Edit: Also, I had been able to run Stasis (2015); so, you definitely have quite a few options, as your hardware is superior.

There's plenty of interesting games that could be played on that machine, depending on what technologies they are built with.

You are mostly limited to older 3D games or modern-ish 2D, although some 2D games are too heavy, like Hollow Knight or Ori and the Blind Forest.

Some modern-ish games I've played on similar hardware:
Bastion - most XNA/FNA games should play fine. Link to the PCGW engine list at the bottom.
Into the Breach - One of my favorite games
Guacamelee - possibly Guacamelee 2 as well.
Fell Seal - Although this game is built with Unity (quite heavy engine) it is shockingly lightweight on resources, being turn based helps. Very very battery friendly.
Battle Brothers - Fantastic game to sink a lot of time, albeit a bit hard to get in the vibe.
Urtuk - Very lightweight as well.
Hearthlands - Also very lightweight, eventually the late game could run slower.
SteamWorldHeist - Runs great. SteamWorld Dig 1 and 2 should run fine as well.
FightN Rage - Very good brawler, gamepad recomended.
Wonder Boy - Very light on resources and battery.

There are more but of the top of my head can't remember them at the moment. Some games might need lower resolution or limit to 30fps to not feel choppy.

Other popular games like Terraria and Stardew Valley should run pretty well but never tried them personaly.

[url=https://www.pcgamingwiki.com/wiki/Engine:FNA]PCGW list[/url]

i can run hunt down the freeman at a playable framarate on my windows 10 4 gb ram celeron on the lowest options btw, though ubuntu sucks it's a shit nuwindows that spys on you, either install artix or gentoo

Darvond's estimate of "up to 2004" seems likely. I had a similar machine in high school, though that was actually worse. It had a Celeron and 4 gigs of RAM. Early to mid 00s ran mostly fine, but the ash storms of Morrowind would impact performance a bit, or turning up the settings in Need For Speed Underground 2. Even the first Half-Life didn't like it if you turned up the details too much.

It will run old games, maybe even slightly modern indies. But don't have too high expectations. The integrated Intel graphics will be limiting.

Keep in mind, you should run away from any game that uses Unity. Crysis probably won't run great either but that's Crysis.

Yes, all games listed below are sold on GOG:

Blake Stone: Aliens of Gold
Blake Stone: Planet Strike
Broken Sword 1 and 2
Commander Keen series
Crystal Caves
Daikatana
Descent 1 through 3
Deus Ex: GOTY
Epic Pinball
F.E.A.R Platinum
Fallout 1
Fallout 2
Fallout 3
Fallout Tactics
Flight of the Amazon Queen (FREE on GOG)
Jazz Jackrabbit Collection (for Jazz Jackrabbit 1 only)
Jazz Jackrabbit 2: Christmas Chronicles
Jazz Jackrabbit 2: The Secret Files
Lands of Lore 1: The Throne of Chaos
Lands of Lore 2: Guardians of Destiny
Lands of Lore 3
Leisure Suit Larry 1
Leisure Suit Larry 2
Leisure Suit Larry 3
Leisure Suit Larry 4
Leisure Suit Larry 5
Leisure Suit Larry 6
Leisure Suit Larry: Love for Sail (yes, it is spelled Sail)
Outlaws and a Handful of Missions
Postal 2
Powerslave (MS-DOS Game)
Quake 1
Quake 2
Quake 3 Arena
Quake 4
Redneck Rampage Collection
Requiem: Avenging Angel
Return to Castle Wolfenstein
Rise of the Triad (or Rise of the Triad: Ludicruous Edition)
SNK 40th Anniversary Collection
Sam and Max Hit the Road
Serious Sam: The First Encounter
Serious Sam: The Second Encounter
Space Quest 1
Space Quest 2
Space Quest 3
Space Quest 4
Space Quest 5
Space Quest 6
Star Trek: 25th Anniversary and its sequel Star Trek: Judgment Rites
Star Trek: Voyager - Elite Force
Star Trek: Elite Force II
Star Wars Dark Forces (Classic, 1995)
Tex Murphy: The Pandora Directive
Tex Murphy: Under a Killing Moon
The Elder Scrolls I: Arena
The Elder Scrolls II: Daggerfall
Thief 1 / Thief Gold
Thief 2: The Metal Age
Tomb Raider 1
Tomb Raider 2
Tomb Raider 3
Tomb Raider 4: The Last Revelation
Tomb Raider 5: Chronicles
Tomb Raider 6: The Angel of Darkness
Tyrian 2000 (Free on GOG)
Wacky Wheels
Wing Commander 1
Wing Commander 2
Wing Commander 3
Wing Commander 4
Wing Commander 5
Wing Commander Academy
Wing Commander Armada
Wing Commander Privateer
Wolfenstein 3D

Could test out Nobara. That uses Fedora and already comes prepacked with graphics and gaming support. So they claim.