Russyo i'm pretty sure that the power wires are different on the Integra. If it was wired correctly, the wiring on the radio harness would be red 12v key on power and yelllow constant like you said.
Wire Purpose - Color/Stripe
Illumination Input - Red/Black
Battery Wire (Constant) - White/Blue
Ignition - Yellow/Red
Antenna - Yellow/White
Ground - Black
I hope you didn't just cut your plug off the car. It's so much easier to just go buy an adapter harness to wire into an aftermarket stereo. Well worth the couple bucks for one. I hated wiring my Integra up because some jackass cut the radio's plug off.
If you are sure the radio works, and the fuse ON the radio is not blown. Check the car's fuse. If both are good, and it is wired correctly check for power at the fuse box. When I was wiring up my CD player I couldn't get power to any of my radio wires. I checked the fuse box and didn't get power there, then I got shocked and had power there and at my radio lol.