We have spent considerable time considering the derivatives of a function and their applications. In the following chapters, we are going to starting thinking in “the other direction.” That is, given a function $f(x)$, we are going to consider functions $F(x)$ such that ${F}^{\prime}(x)=f(x)$. There are numerous reasons this will prove to be useful: these functions will help us compute areas, volumes, mass, force, pressure, work, and much more.