It would be way too hard to swap that engine into your car, Im not saying it can't be done, but you would have to buy a crapload of stuff to make it work. The short list would be:
hasport ekstk mount kit ($450) with hasport egbcc ($200) these would be the mounts you would need to put the engine in the car, you would also need a rear engine bracket from 2000 civic Si (b16a2) (50-75 bucks)
you would be able to use the axles from the integra but you would need 94-01 integra shift linkage (100-200) in order to shift.
so you are at about 850
next comes the wiring: you would need first to get an ecu to run the car, pr4 ecu from a 98 integra would be optimal, (about 150) then you would need obd2 fuel injectors (100) and a wire harness if you dont have one (not sure on that price) and lastly an obd1 distributor for 92-95 integra(250)
so now you are over 1200
you will have to be pretty handy with wiring because some wires need to be run/changed for the distributor since the obd2 crank sensor would be on the oil pump while the obd1/0 has it in the distributor. You would have to re-wire the entire distributor and then run those 2 wires for crank sensor back to the dizzy.
After all of that you still run into the problem that you might end up with a check engine light for emissions since the obd0 integra engine would have any of the emission stuff that the newer ecu would look for
After all of that I cant guarantee youthat your top engine mount would work right because they changed them and the hasport mount kit doesnt specify if it supports the older b series engines.
Either way it would be well worth your time to find a complete swap from a 96+ integra, it would make your like alot easier.