My advice, is obviously to calculate the fourier transform of these functions, and then use the convolution formula, but in this case use the fact that exp (i b k)=cos(bk)+isin(bk) to replace this with sin(bk) in the integrand.

if f(k),g(k) are the fourier transforms of f(x),g(x), and h(z) is the convolution of f and g then, then h(x)=F^-1(f(k)g(k)) where F^-1 is the inverse fourier transform.