the integrated GPU is part of the southbridge. It should already have a cooler on it.
If I were you, I would suggest that you just save up to get a dedicated card and not worry with trying to improve the onboard performance.
What 400W unit do you have, and what are the rest of your system specs?
A Dynex 400W PSU , I have 4 gigs of DDr2, this mobo http://us.test.giga-byte.com/Products/Motherboard/Products_Overview.aspx?ProductID=3454, and a 320 gig HD.
maybe a 5570 or GT 440? they wont give you stellar performance in crysis, but will be better than the 4200.
Is there any reason that you dont want to upgrade to a better PSU? You will get better performance if all of your parts are getting adequite power. I suggest a 550 or higher.
I wouldn't put either of those, or any video card for that matter, in with that PSU, period. I'm not saying it wouldn't work, but it would be extremely reckless to suggest it or to do it at all.
Spend your money first on a new power supply, then on a video card. What is the point in getting a video card that you then won't be able to use, or going half arsed on your parts and have them not perform as you want them?
I am getting this PSU http://www.newegg.com/Product/Produ...m_re=power_supply_650w-_-17-702-018-_-Product and the EVGA card you recommended.
No, do not.
BFG are out of business, so you get no warranty. It also isn't a great unit. BFG did make some good power supplies, that is not one though.
The saying "you get what you pay for" applies, and by getting that unit, you may as well just stick with what you have, because it isn't a whole lot better. $40 for a 650W unit should start making alarm bells ring, even if you don't know anything about what to look for.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817371047
or
http://www.newegg.com/Product/Product.aspx?Item=N82E16817256071
+
http://www.newegg.com/Product/Product.aspx?Item=N82E16814500202
Comes out to $187 after rebates, $217 before, and it is a hell of a lot better