integrated graphics for the sims 3?

Yes, the Intel i3-2105 with HD Graphics 3000 should play Sims 3 at medium to high graphical settings with no problems at all.

For Sims 3, no you do NOT need a "good graphics card." It was designed to work with integrated graphics way before the Intel HD was released. Sims 3 was released in 2009 when most people utilising Core 2 Duo/Quad's were still considered in the high-end tier; even then most people didn't have a C2D/Q, where Sims had low system requirements to begin with. Sims 3 requires a Pentium 4 (P4) at minimum, where the P4 was released on the 20th of November 2000 (that in technology years would be considered B.C!)

Your processor, coupled with it's integrated graphics should have no problem running Sims 3. Sims 3 is not a demanding game, it has been "moulded" to operate on systems' with low specifications. As you're on a tight budget, you're all set to build and play Sims 3 at a good frame rate, and your computer will run circles when you're just using it for daily use (i.e. web browsing, document editing, presentations etc.)

However, I'd keep your first build and upgrade it later when you have more funds to spend. Your computer can be upgraded later, which I believe will save you costs in the long run when you seek more performance. With that said, I have noticed you're going with a motherboard on socket 1155 and a Sandy Bridge (2nd generation) processor. At the moment we're on the 4th generation (Haswell), and to be honest, the i3 you've chosen is great, however if you truly want more performance in the future, you could upgrade your CPU. But you'll be pretty limited if you stick with a 2nd generation processor, and if you desire to upgrade to a 3rd (Ivy Bridge) or 4th generation CPU you'll need a new motherboard. However! There are some motherboards which support both 2nd and 3rd generation. I'd recommend you pick up one of those motherboards (it'll still be compatible with your Intel i3-2105; I'd still double check with the CPU support list for the motherboard you chose however to be safe.)

The motherboards which are compatible with both 2nd and 3rd generation CPUs are those with the following chipsets: H61, H67, P67, and Z68. CPU support will vary however, you will need to look up the motherboard's manufacturer's CPU support list specifically for your motherboard. With a motherboard with one of those chipsets, you'll be able to upgrade to a 3rd generation (Ivy Bridge) processor at a later date, giving you a major performance boost and also saving you costs in purchasing a new motherboard, as well as other compatible components you may require if you were to purchase a new motherboard.

Regardless before we get into CPU upgrades, simply ensure you're on one of those chipsets. Then for your next upgrade to your machine, install a graphics card, then focus on the CPU. As long as you adhere to my suggestions, you should be prepared for the future whilst on a tight budget.

All the best.

Well, you'd probably be better off with Kaveri if you go the integrated route, but an i3 2105 should be able to handle the Sims 3 at medium settings.