$$\int_a^b f(x) dx = F(b) - F(a)$$

Where F() is the anti-derivative of f()

$$\begin{align*} \int_a^b x^2 dx &= [\frac{x^3}{3}]_a^b \\ \\ &= \frac{b^3}{3} - \frac{a^3}{3} \end{align*}$$