Fundamental Theorem of Calculus

Let $f(x)$ be a function of one variable. Then the fundamental theorem of calculus states that:

$${\int }_a^b\frac{df(x)}{dx}dx=f(b)-f(a)$$

We can also write this as

$${\int }_a^{b}F(x)dx=f(b)-f(a)$$

When we set $\frac{df}{dx}=F(x)$. To integrate a function $F$, just think up a function $f(x)$ whose derivative is $F(x)$.