Calculus I provides the basic concepts and tools for solving many useful problems in physics, other natural sciences, economics and a host of other disciplines. The derivative is a fundamental concept because so many modeling problems involves rates of change. Integration is the key to solving equations that involve rates of change as well as solving great stuff like areas, volumes, and arc lengths.

In Calculus II the study of Calculus first turns its attention to applications of integration followed by integration techniques that greatly extend the possible functions that can be easily (?) integrated.