From The Ramanujan Journal, 5 (2001), no. 1, 73-89.

Abstract.
Using Fourier transform techniques, we establish inequalities for integrals of the form $$\smallint _0^x \prod\limits_{k = 0}^n {\frac{{\sin (akx)_{} }}{{akx}}dx.} $$
We then give quite striking closed form evaluations of such integrals and finish by discussing various extensions and applications.