Area between curves

$\int _{a}^{b}(upperfunction-lowerfunction)\,dx,$

if f(x) = upper function and g(x) = lower function

$\int _{a}^{b}(f(x)-g(x))\,dx,$

example

ex1: $\int _{0}^{2}(2x-x^{2})\,dx,$

f(x) = lower function

g(x) = upper function

f(x) = $x^{2}$

g(x) = $2x$

$\int _{0}^{2}(2x-x^{2})\,dx,={2x^{2} \over 2}-{x^{3} \over 3}\int _{0}^{2}$