Fourier Series Limit proof

I'm working on a problem at the moment and I just can't figure it out, here goes:

$\displaystyle \lim_{n \rightarrow \infty } \frac{1}{\pi} \int_{-l}^l f(x) \frac{sin(nx)}{x} dx = f(0) $

with l > 0 and f(x) differentiable on the interval [-l,l]

Things that come to mind are Riemann-Lebesgue Lemma -- from Wolfram MathWorld Riemann's lemma which states that any limit of n to infinity of an integral of a function on -l to l of the function times sin(nx) or cos(nx) tends to 0.

And ofcourse that $\displaystyle \int_0^{\infty}\frac{sin(x)}{x}dx = \frac{\pi}{2}$

Does anyone have any ideas on how I can proceed?