0
its an non integrable function
The indefinite integral of exp(x^2) dx is
1/2 * sqrt(pi) * erfi(x) + K
where erfi(x) is the imaginary error function, defined with regard to the error function as
erfi(x) = - i erf(ix)
see http://mathworld.wolfram.com/Erfi.html
Also, try wolframalpha.com, enter
exp(x^2) in the search box or
int(exp(x^2),x)
to see some plots and other info.
Answere^(x^2) is an example of a function expressible using standard functions (+, *, exp, log, atan, etc) whose integral can not be expressed in this way. In such cases we invent a name for the function defined by the interval, but it's just a name and doesn't shed any light on the function. In short, there is no intellectually satisfying answer to this question.
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