So i downloaded the game using the Gog Client when i run it the integrity check comes up and it doesn't move sooo i dont know what to do

i tried skipping the check then it said i had a corrupt file

Your best bet is probably to re-download. If you were using the GOG Downloader then you could try downloading with your browser instead and see if that works better.

Sometimes integrity check cannot complete if you aren't running the installer as an administrator. But, as Waltorius wrote, it may be as well corrupted download.

Well, it would be unexpected to find that the file is corrupted because one of the features of gogdownloader is to ensure that corruption will never occur during download. The downloader is making an automatic integrity check for each download chunk and one final check for the entire file. So it seems to me unlikely to have a corrupted file unless there is a bug in the gogdownloader, or you have transfeed the downloaded file trough a network or drive and that corrupted the file afterward.

Try what Thiev said, run as admin and see what happens. Anyway, integrity check for the witcher takes a while so make sure you are patient.

As a supplementary measure temporarily disable any program likely to interfere with the installer, like antivirus for example.

If you changed the destination folder after adding the game to downloader, that may also cause the check to fail.