Well the spark plug wires were bad and putting in new plugs and wires made the car idle and run great.
Last Saturday I was driving the Integra over to my mom's house to change the oil and replace the stuck-open thermostat. I was about six blocks from home when I heard a weird noise and the car lost power.
I pulled into a Burger King parking lot and checked under the hood. There was a hole in the valve cover where the timing belt was. Inside the hole I could see that the belt was starting to come apart.
I had the car towed to my mom's house, pulled the valve cover off and took a look. It looked like the cams stayed in time.
I tore the side of the engine down for a t-belt swap. Everything was going well until I took the cam pulleys off for better access to the water pump. When I put one of the cam pulley bolts back on I overtorqued it and broke the bolt off inside the cam.
I was able to get the bolt extracted with a reverse drill bit. My brother and I found an identical replacement bolt in a junkyard 1990 Accord.
We put the water pump, t-belt and crank pulley back on and gave the car a test start. It started right up and went into a nice smooth idle.
It has been raining the last couple days so I still have to replace the timing covers and accessory belts and give the car back to my little brother.