Find $\displaystyle \alpha$ such that the following differentiation formula holds:

$\displaystyle f'(x) \approx \alpha \int_{-h}^h t \, f(x+t) dt$

So first thing I did was tried to integrate using integration by parts

$\displaystyle \int_{-h}^h t \, f(x+t) dt = [t \, F(x + t) ] ^h _{-h} - \int_{-h}^h F(x+t) dt$

but I don't think that's right. I'm trying to get it to look like $\displaystyle \lim_{h \rightarrow \infty} \dfrac{f(x + h) - f(x)}{h}$ so I'm guessing $\displaystyle \alpha$ has a limit in it?

Can anyone help?