There is a very common problem with the Corolla that causes this. It is a dirty MAF (MassAirflowSensor) and it can easily be cleaned. There are several guides on the web, Google "Toyota corolla maf sensor". Expensive electronics cleaner is not needed, Isopropyl alchohol and a Q-tip will work fine. You will need a scanner to reset the EngineCheckLight (Autozone or a friend) or I think it will automatically reset after about 40 times you start the car? This is a 10minute repair. For some reason most professional mechanics do not know how to Google!