SL 5.5—Integration introduction, areas between curve and x axis

Integration is the reverse process of differentiation. If differentiation takes a function and finds its rate of change, integration goes the other direction , given a rate of change, it recovers the original function. For this reason, integration is often called anti-differentiation.

Anti-derivative: A function $F(x)$ is called an anti-derivative of $f(x)$ if $F^{\prime }(x)=f(x)$. In other words, differentiating $F(x)$ returns $f(x)$.

For example, since $\frac{d}{dx}(x^3)=3x^2$, we know that $x^3$ is an anti-derivative of $3x^2$.