Explain if image stabilization on DSLR comes from body or individual lenses?

I'm in the process of choosing a dslr.looking at nikon d3100 or canon rebel.t2i. I've read many contradictory things. So I'm confused about which is the better camera. I'm also confused about image stabilization. Some info seems to indicate that some cameras have it built in, so any lens you attach will maintain stabilization… On the other hand, I also see some actual lenses have stabilization. Can someone advise me?

The main important stabilization system is on the lens.
For the Canon Lens, those ones are named IS (image stabilization).
Don't know about the Nikon ones.

That's manufacturer dependent.
Canon and Nikon build the image stabilization into their lenses, at least for SLRs. This has the advantage that the stabilization is optimized for that particular lens, and you can see it working in the viewfinder.

Pentax and Sony use so called sensor shift image stabilization, which is built into the body. You can't see it working in the viewfinder, but it works with every lens that is mounted on the camera.

For point and shoot cameras, all brands use sensor shift stabilization as far as i know.

Canon & Nikon do not have image stabilisation built into the camera body (Pentax does), it's in the lenses that are marked IS (Canon) or VR (Nikon).

Generally speaking, image stabilisation mechanics work better when they are in the lens, as they are tailored to that particular lens and are therefore very specific - this makes the stabilisation far better.

The Canon T2i and Nikon D3100 are both good cameras - in terms of which is best for YOU, I suggest you go into a camera store & try both of them - for weight, button position, ease of use of the menu. Take a few test shots & look at viewfinder brightness, image quality - then decide.

Some brands have stabilisation built-in to the camera body, but not Canon or Nikon. Probably Sony and Pentax, maybe others.

With Canon it comes with the lens (depending on the type). A cheap fix is to use a tripod or monopod