If I were you, I would add an AMD 7750 to my PC. Very low on power requirements, very inexpensive, and almost certain to work with your build. If I am not mistaken, you don't even need a PCI-E connector. The instillation couldn't be easier - it just pops right in.
Here is an excellent one right here...http://www.amazon.com/Sapphire-11202-00-20G-Radeon-PCI-Express-Graphics/dp/B007B5V614/ref=pd_cp_pc_0
$100 (after $10 rebate).
You should be able to play most games at decent visual detail and at a fairly high resolution.
And it would blow the hell out of any integrated solution.