Pillar 5: The whole change is the sum of the partial changes

The difference between a baby and an old man is the sum of 30,000 tiny day-to-day changes. Functions work the same way. You can get the total change in a function by adding up (integrating) its rate of change (derivative). Likewise, we can get a function by differentiating its integral. This is called the Fundamental Theorem of Calculus, and gives us an incredibly powerful way to compute integrals.