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How to compute $ \int_0^1 {e^{-x^2}} dx$
I know that
$$
\int_{0}^{+ \infty} e^{- x^{2}} dx = \frac{\sqrt{\pi}}{2}.
$$
My question is:
$$
\int_{0}^{1} e^{- x^{2}} dx = ~?
$$
