This is one of the better integrated solutions. If it's not up to the task, I'd pick the under 100 buck card from this list -> http://www.tomshardware.com/reviews/gaming-graphics-cards,1965.html
Your 6200 should be left in the dust even using the under 100 dollar card noted.
I am getting a new computer on Tuesday and it is already ordered and payed for. I play some games one of them is the Sims 2 (I have all expansions but Free Time) and I play Roller Coaster Tycoon 3 sometimes. This is the computer I am getting http://www.bestbuy.com/site/olspage.jsp?skuId=999993200050019&type=product&id=pcmprd93300050019
Does anyone know if I can play the game without needing another graphics card? The one currently in this system is the 256 mb geforce 6200, but it's an agp card (which I probably can't put in the new one). Thank you.