Can you swap a B20 in a 91 integra LS with stock transmission?

Yes. The 91 ls came with a b18 and that engine shares it's block with the b20. The new engine will drop in, but you will have to swap out some of the parts off of your old engine such as intake manifold, distributer, fuel rail, etc. The only modification you will need will be to extend the temp sensor wires to reach the new location by the thermostat housing as your old sensor is on the rear of the block. You can use your old motor mounts, transmission, harness, belt etc. on the new engine, and any bolt on modifications for the original engine will fit the b20 as well. The transmission bolts right up with no problems.