The HD 4200 is integrated, although it sometimes has dedicated memory (known as Sideport memory). It's still slow ...
The HD 4330 is definitely better, but still an entry-level discreet card ...
http://www.staples.ca/ENG/Catalog/ca...affixedcode=WW
Much better card for a much lower price. HP > Gateway as far as reliability goes, though (not a huge difference, but still).