Where is my graphic card located in my PC? (Pic inside)

The black slot is usually PCI-E 16x. You can tell if you see only two sections, a small near the computer case and a large after (see picture below). AGP would have three sections, about the same size. Installing a discrete graphics card automatically disables the onboard graphics in most motherboards, so you don't need to go into BIOS to do it manually. In some motherboards you can keep the onboard enabled to use it for multi-monitor setup, the discrete card takes priority by default (is the one to give picture to the monitor during boot). OF course you will have to install new graphics drivers for your new card. Go directly at nVidia or AMD to get latest drivers. Do not rely on DVD-ROM or Windows Update.

I cant get a better quality picture ... The reason i was gonna try to swap becuz the Intel HD Grapics Card is lil better than the Intel G41

You cannot swap onboard graphics, but you can add a new PCI-E graphics card. There is no need to be something expensive, the entry level nVidia or AMD should be OK and faster than Intel.

Yep, your best bet is to install a graphics card in the computer that you want to upgrade.

If you buy anything between the entry level and medium graphics card, you shouldn't have space problem. If you buy medium to high end you will also need a new power supply.