Pretty much what enkoujin posted. Calc I is limits, derivatives, and an intro to integration. Calc II is a continuation, so formal integration, infinite series, and an intro to vector (linear) algebra.
The first two classes don't teach you any of the shortcuts right away, because you're learning the method and theory behind them (as how limits lead to derivatives). That makes them a pain because you have to do everything the formal way until the end of each topic.