If you really one to setup a forum for your site, go get phpBB2 or InvisionBoard or better, buy vBulletin. eZ publish is too powerful for a forums, or too slow for a forums :D
Hi, The question is not "Is it possible " but rather how long will it take. I have heard of people adding some other forum to and ez-site, I dont remember what forum or who did it, but there may be a post about it on the forum somewhere. It was a german site, and it looked nice. Also from your question rises another one, how integrated do you mean? Do you have specific needs?