Integral of inverse erf from 0 to 1

Theorem

The following formula holds: $$\displaystyle\int_0^1 \mathrm{erf}^{-1}(x) \mathrm{d}x=\dfrac{1}{\sqrt{\pi}},$$ where $\mathrm{erf}^{-1}$ denotes the inverse error function and $\pi$ denotes pi.