Plumba, I read something might be interesting to you.
II. H22A Swap
Another way of achieving 2.0L or more in an Integra is to swap for an H22 engine, ECU-VTEC wiring harness, and tranny.
The downsides are :
a) The H22A and tranny will add at least 100 lb to the front of your Integra compared to a Bseries engine and to some people this is not important. However, the polar moment of inertia (i.e. how easily the car will turn/spin based on weight distribution) is drastically changed and the cornering speeds will be reduced since you won't make turns as fast without ploughing forward with understeer.
b) you will lose your A/C and power steering (or relocate the A/C) to make room in the engine bay for this engine and tranny.
c) you are stuck with the H22 tranny. Unlike the B series where you can mix and match stock trannies with different gear ratios, final drives, and LSDs, you have only 1 choice.
If these are not a big deal to you then the same rules for putting an H22 into a Civic apply. For 3rd generation Integra owners, you will need either a 90-93 Accord left side axle intermediate shaft with a 90-93' Integra left axle or you can use both 90-93' Integra driveshafts. The best way to go is to purchase stronger aftermarket driveshafts made for the Gen.2 Integras from someone like Frank at
http://www.driveshaftshop.com/vtec.ivnu (whose product I have personally used and highly recommend ) or
http://www.raxles.com (who also come well recommended by fellow racers)
You will need a HASPORT or PLACE RACING mounting kit and basically will need to shave off the tranny side mount bracket. There's no need for the top tranny mount bracket, since it bolts on from the bottom of the frame.