Does a CPU have a GPU built into it

You can only use the integrated graphic core if your motherboard has an Intel H series or Z series chipset. The Intel P series does not allow you to use the integrated graphic core.

Additionally, if your PC is mostly used for gaming and you do not use any media creation / editing software, then you are actually better off with the less expensive i5-2500k which allows you to overclock the CPU. The vast majority of games do not make use of Hyper Threading. I believe BF3 maybe one of the handful of games that can make use of Hyper Threading (HT). However, I've read conflicting stories on this issue because some players have stated they needed to turn off HT because it caused BF3 to stutter.