You're quite right - Intel Extreme Graphics is an integrated graphics chipset, found on many modern intel motherboards. You will definitely be able to upgrade your graphics, the only question is what kind of slots you have available for upgrading.
Your best option, if available, is an AGP graphics card. If you can, have a look at your motherboard and note down the following:
Does it have an expansion slot that is set slightly further away from the edge of the motherboard and is brown in colour (very common for AGP slots to be brown)? This slot is always the closest slot to your processor (which will be hidden underneath a huge heatsink/fan combination). It will be paralell to any (usually) white PCI slots you may have - which will run down the motherboard to the edge (often 4-6 PCI slots). You'll at least then know immediately if you have an available AGP slot.
If you do, also note down the model number of the mother board. This is usually in the centre of the board, normally about 6-12 alphanumberic digits. You can also determine the model number of your board by booting your computer and paying attention to the text that appears on bootup - it will almost certainly be near the top left hand corner of the screen. With this number, by checking the manufacturers website, you can determine what TYPE of AGP slot you have. AGP slots come in 1x, 2x, 4x and 8x varieties - the higher the multiplier, the faster card the motherboard is capable of supporting. You can then go out and buy your new card!
Of course, if you don't have an AGP slot your only option is to upgrade with a PCI-slot graphics card - a less attractive option as not as much data can flow through the PCI bus as opposed to AGP bus, limiting the upgrade you are able to perform.
