Random Mathematics - Calculus Practice

$\displaystyle\int_{-a}^a f(x)\,dx = 2\int_0^a f(x)\,dx$, if $f$ is an odd function

$\displaystyle\int_0^{2a} f(x)\,dx = \int_0^a f(x)\,dx - \int_0^a f(2a+x)\,dx$

$\displaystyle\int_a^b f(x)\,dx = \int_a^b f(a+b-x)\,dx$

$\displaystyle\int_{-a}^a f(x)\,dx = 0$, if $f$ is an even function