Integrate $I= \int \limits_0^1 e^{x^2} dx$

Question

\[\begin {array} {1 1} (a)\;I \in (0,1) \\ (b)\;I \in (e, \infty) \\ (c)\;I \in (1,e) \\ (d)\;I \in (1,\infty) \end {array}\]