If you have a B18C, you will have problems installing that in a '90 Civic. It will not bolt in, you will need an aftermarket bolt-in kit. Also, your car's clutch is controlled via a cable while the '94+ Integra's are hydraulic. You will need to find B-series cable transmission, preferably from an older JDM B16A equipped car (that will also have a cable tranny) as it's gearing will better match the B18C than the B18A non-VTEC LS motor's cable tranny will. Also, your car uses OBD-O or pre-OBD electronics (same thing, different names) while the B18C is OBD I or II depending on what year and car it was from. You will either need an aftermarket ECU or convert your engine wiring harness to work with an OBD I ECU. If your car is not an SI, you will also need to convert from DPFI (Dual Port Fuel Injection, IE 2 by the throttle body) to MPFI (Multi Port Fuel Injection, IE 1 injector per cylinder).

Long story short, your going to have some work ahead of you. If it's not too late, you may reconsider and purchase a first generation B16A that will come with a cable tranny, pre-OBD electronics and ECU. The smaller displacement will produce less torque and less hp but the B16A will be much cheaper and much easier to actually get the car running. Good luck with it.