Prove that $\int \limits_0^{2a}f(x)dx=\int_0^a[f(x)+f(2a-x)]dx$ How do I attempt this? What is the aim of the proof? 
I've been trying silly things with the LHS and the RHS but cannot produce anything of use. 
Can someone offer a very slight hint on proceeding?
Thanks
I did this so far:
$\displaystyle \int \limits_0^{2a}f(x)dx=\int \limits_0^a[f(x)+f(2a-x)]dx = \int \limits_0^a f(x)dx + \int \limits_0^a f(2a-x)dx$

$$\int_0^a f(2a-x)dx = \int_a^{2a} f(y)dy.$$
