The Concept of the Antiderivative
Big Idea: If differentiation answers "What is the rate of change?", then antidifferentiation answers the reverse question: "What function has this rate of change?"
1. Motivation — Reversing the Derivative
You already know how to differentiate: given a function $f(x)$, you can find $f'(x)$. But what if someone gives you a function $g(x)$ and asks: "What function, when differentiated, gives $g(x)$?"
This reverse process is called antidifferentiation, and the result is called an antiderivative.