An integrated video soltion is seldom adequate for any but the more rudimentary games, none of the hot titles.
The expansion you have depends on the motherboard and power supply.
http://h10025.www1.hp.com/ewfrf/wc/document?lc=en&cc=us&lang=en&product=1817038&dlc=en&docname=c00361570That is your machine. Besides integrated graphics it has no AGP and certainly no PCIe slots, so all you are left with only standard PCI. You will find little joy in that, but if you DO manage to find some card that meets the game requirements in standard PCI, then you will have to make sure that the power supply can handle it. That one has only a 300w PSU. It may be able to take a larger one if it is not proprietary, but you would have to check with HP on that.
In short, that machine will do what it was intended to do which is word processing, e-mail and internet with no problems. It is not a gaming rig and will not ever be one. Sorry.