Prove that:

a) iff(x)is an even function, $\displaystyle \int^a_{-a}f(x)dx=2\int^a_0 f(x)dx$

b)iff(x)is an odd function, $\displaystyle \int^a_{-a} f(x)dx=0$

I tried using proof by contradiction:

f(x)is even, then $\displaystyle \int^a_{-a}f(x)dx\neq 2\int^a_0 f(x)dx$

My problem is I don't know how to continue.

I figure if I get the first one right I can do the other.

Thanks!