Hi

I am trying to prove that

F(f(x))=-2i*int_from 0 to infinity(f(x)*sin(2*pi*x*gamma)dx)

I have already made it out to be

int_from -infinity to infinity(f(x)*(cos(-2*pi*x*gamma)+i*sin(-2*pi*x*gamma))dx)

the question is what happens other than cos(...)=0 because f(x) is an odd function? What really troubles me is how sin(-2*pi*x*gamma) becomes sin(2*pi*x*gamma).

Thanks in advance