Show that if a random variable has the probability density

$\displaystyle f(x) = {\frac {1}{2}e^{-|x|}}$ for -∞ < x < ∞

its moment-generating function is given by

$\displaystyle Mx(t) = {\frac {1}{1-t{^2}}}$

I know that I need to find the integral, but I am getting confused. Could you please help?!