In the last chapter we studied derivatives. As you know, the derivative of a function allows us to study the rate of change of the function. For instance, when we modeled the height of an incoming missile with the function g(x), the derivative of the model, g'(x), was a model of the rate of change of height of the incoming missile. In this chapter, we study the opposite process, called the integral. The very short story goes like this: if we construct a functional model of the rate of change of some physical quantity, the integral of the function will tell us the accumulated effect of that rate of change. For instance, think about the model of the rate of cars (in cars per minute) traveling along Route 15 in Johnson, Vermont. The integral of this model will give us insight into the total number of cars that travel along Route 15 during a period of time. In the next few lessons, we'll refer to the total number of cars that travel along a road during a period of time as a "car count". One unfortunate fact is that the mathematical definition however is quite different than the interpretation that is described above. One of the main goals of this chapter is to help you connect the interpretation of the integral and its mathematical definition. The integral and the derivative together comprise the two core ideas of calculus. You already know a lot about the derivative. Click ahead to get started learning about the integral!