automatic transmissions don't have clutch and a pressure plate. they have a torque converter. the 89 integra doesn't come with b18b1 like the 94+ integra do, so i doubt it will bolt up.Your clutch set up would be different. Your car should have a cable clutch, whereas the '96 would have a hydraulic one. As for the actual engine I would think as long as the engine would be the same.
I wouldn't go for it if I were you.