The Integra actually came with two different ECUs.
If you took the engine out of a 90-91 Integra, it is in fact an obd0 ECU called the PR4.
The 92-95 Integras also had the PR4, but were obd1, the earlier models coming with the b18a1, later models coming with the b18b with a p74 or p75 ecu, depending on what year it was made and what trim it had.
You can also use other ECUs if you've done the swap already, but basically want to line up your on-board diagnostic system of the engine to that of the car. If you have an obd0 b18a1, you should try to get the wiring harness (going to the dash, called the "chassis harness") from the Integra, and wire that into your Civic. Otherwise, it's possible to convert your B18a1 over to obd0 if need be, but I'm not sure where those articles are and they seem to have mixed reviews. I suggest trying to get the full wiring harness from either your car or your engine and go with the ECU that works with the obd you're working with.