We have spent a lot of time learning how to take a function and find its rate of change — its derivative. Now we turn that question around. What if we know the rate of change, and we want to recover the original function? That is half of this chapter. The other half asks a seemingly different question: how do we measure the total accumulation of something over an interval, like the distance travelled by a car whose speed keeps changing? By the end, you will see that these two questions — going backwards from a derivative, and measuring accumulated area under a curve — are deeply connected.