Integral : The integral of a function $f$ between $a$ and $b$ is defined as $\int\limits_{a}^{b}f(x)dx$ $=\lim \limits_{n\to\infty} \frac{(b-a)}{n}\sum\limits_{k=1}^{n}f(a+\frac{k(b-a)}{n}).$ For example $\int\limits_{a}^{b}xdx=\frac{b^2}{2}-\frac{a^2}{2}.$ The fundamental theorem of calculus provides a simple way to calculate integrals using antiderivatives.