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) = $2x$

Failed to parse (unknown function "\ove"): {\displaystyle \int_{0}^{2} (2x - x^2) \,dx,= {2x^2 \over 2} - {x^3 \ove4 3 } \int_{0}^{2}}