You have to use the conditions on even and odd functions. I would then break up both LHS integrals into two pieces: one on either side of the origin.
a) if f(x) is an even function,
b)if f(x) is an odd function,
I tried using proof by contradiction:
f(x) is even, then
My problem is I don't know how to continue.
I figure if I get the first one right I can do the other.