I=\int_{\frac{1}{\sqrt{2}}}^{\infty } e^{-t^2} \, dt=\sqrt{\frac{\pi }{2}}\mathrm{Erfc}\left(\frac{1}{\sqrt{2}}\right)=\sqrt{\frac{\pi }{2}}\left(1-\mathrm{Erf}\left(\frac{1}{\sqrt{2}}\right)\right)