X has uniform dist (0,1).

I found the MGF to be:

$\displaystyle \frac{e^s - 1}{s}$

Now I need to expand the MGF in powers of s up to $\displaystyle s^2$ and use this to find the mean and variance of X. I know the series expansion for $\displaystyle e^s = \Sigma \frac{s^r}{r!}$, but I'm not sure how to apply this in this situation.