Too many engine faults could cause misfire trouble codes P0301 and P0303.
P0303 Cylinder 3 misfire detected
P0301 Cylinder 1 misfire detected
In terms of repairs, either you or a California certified smog check repair station can diagnose and fix the problem(s) causing your Acura Integra's misfires. If your local Acura dealership is "smog check repair" certified by the State of California they are allowed to repair your vehicle as well.
We'd recommend you begin by ensuring your Acura is in proper fuel control and that the misfires are not caused due to lean or rich fuel mixtures. This requires checking voltage from the oxygen sensor, ensuring the signal gets to the ECU, and that the ECU is in proper control of the fuel injectors.
Next you want to ensure your Acura's spark plugs, wires, cap, and rotor are in good condition. Misfires are often caused due to defective engine ignition components.
High cylinder compression and even a faulty camshaft position sensor would cause misfires as well.
So you can see there are plenty of components which need to be inspected. Misfires are some of the hardest faults to diagnose. In our opinion, it is best left to the experts.
