Are you looking for steps to arrive at the answer or just the answer? If the latter, then I suspect you want to integrate using what Luis Ledesma wrote but from minus infinity to plus infinity which results in
$\sqrt \pi$. (This integrand is proportional to the standard normal probability density so if there are other limits of integration needed, then you might want to look at the standard normal cumulative distribution function.)
Integrate[E^-x^2, {x, -Infinity, Infinity}]
