Non-Elementary Integration · Easy problem

The function $e^{-x^2}$ has no elementary antiderivative, but its integral over a half-line is known. Given $\displaystyle\int_{-\infty}^{\infty} e^{-x^2}\,dx=\sqrt{\pi}$, evaluate $\displaystyle\int_0^{\infty} e^{-x^2}\,dx$.