Well whatever aftermarket HU your buys, you know there's a wiring kit for the HU. Now depending on where you buy it, you can ask them to hook you up for a kit for your friend's integra. Most places are really happy to do that for you. If you do have to pay for one, it'll costs you nomore than $15.

Don't solder the wires togethers! haha Use vinyl insulated butt connectors. Usually when you buy the kit, you'll get them.

In terms on get the HU out, you're stuck. Haven't worked on an integra, but if it's anything like the 94' accord, you have to take the cover out inorder to unscrew the HU. Try looking around the HU for screws you might think it holding the dash cover. You might have to pop off the clock to see if there's a screw. Well g' Luck!