1998 acura integra LS motor will drop right into a 95 cx, and the wiring harness off the engine will plug right into the cx chassis at the shock towers.
Use the throttle cable from the integra, also use the axles, shift linkage and all engine mounts.
make sure that when you remove the cx engine from the car that you don't open the clutch hydraulic system, just simply remove the clutch slave cylinder from the cx tranny prior to engine removal and hang it out of the way.
you are going to need a radiator out of a 94-97 del-sol dohc vtec, or out of a 99-00 civic Si dohc vtec.
use the integra radiator hoses with this radiator.
You will also have to get an obd1 integra LS ecu p75 I think (check under swap info in the refrence section for the 94-95 integra obd1 ecu), the 98 ecu out of the integra will not work due to it being obd2 and the car being obd1
the honda civic CX used a 1 wire 02 sensor so you will have to run new wires to the ecu for the 02 sensor, you can find the ecu pinouts in the refrence materials section at the top of the forum
Swapping the dashboard into the civic will have its own set of problems with fitment and possibly wiring, I haven't done the integra dash into a civic, but I have seen it done, I do know however that there will be fitment issues with the door panels and the dash.
Also, if you want a good upgrade, remove the front steering knuckles with the rotors and calipers from the integra and put them on the cx, it will give you a larger disc brake in the front
you can also remove the rear suspension from the integra and put that on the civic and have 4 wheel disc brakes. (direct bolt on and you will get to use the rear sway bar if you want)
if you really want to go wild you can take and remove the radiator support from both cars, (lots of drilling) and put the integra radiator support on the civic (lots of welding) then take the hood with the brackets from the integra and put that on the civic, then the headlights, front bumper and fog lamps (if equipped). then take the fenders and have someone who is really good at body work cut the fenders and weld them together and do all the body work and then you can have a full integra front clip on your car.
the possibilities are endless.
Have fun and ask any questions that I haven't answered in the forums.