with that of your arm => to that o your arm

Doesn't "to that" go better with "incorporate" instead of "incorporate A with B"?

gu76)When you use a tool, your brain thinks of it as an actual extension of your body. For example, one experiment demonstrated that after performing tasks with a long mechnical grabber, people behaved as if their arm were longer.,,When you brushed your teeth this morning, you didn't have to look at your mouth or your arm because your brain has fully incorporated the idea of the toothbruth with that of your arm...

To does not work and with is not very good either. The best preposition here is into. Incorporate comes from the Latin corpus, corpore meaning body. It means to merge something into something else.

The example you gave is one of the most literal I can think of. Your toothbrush became part of your arm.