Non-Elementary Integration · Easy problem

Given $\displaystyle\int_{-\infty}^{\infty}e^{-x^2}\,dx=\sqrt{\pi}$, find the constant $c$ that makes $f(x)=c\,e^{-x^2}$ a probability density on the real line, that is, $\displaystyle\int_{-\infty}^{\infty}c\,e^{-x^2}\,dx=1$.