Definite Integral of $e^{\large x^2}$ I know there's no elementary antiderivative of $e^{\large x^2}$.
But what if there's a definite integral like 
$$\int_0^1e^{\large x^2}\ dx\ ?$$
I tried using basic definite integral property like $\displaystyle\int^a_0f(x)\ dx =\int^a_0f(a-x)\ dx $ but I could see no way out.

Hint: check how the improper integration of $\int{e^{-x^2}}$ happens, and use an $x\rightarrow{ix}$ mapping.
