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If \( \mathrm{S} \) be the area of the region enclosed by \( y=e^{-x^{2}} \), \( y=0, x=0 \), and \( x=1 \). Then
[IIT-JEE 2012]
P
(a) \( \mathrm{S} \geq \frac{1}{\mathrm{e}} \)
(b) \( S \geq 1-\frac{1}{e} \)
(c) \( \mathrm{S} \leq \frac{1}{4}\left(1+\frac{1}{\sqrt{\mathrm{e}}}\right) \)
(d) \( \mathrm{S} \leq \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{\mathrm{e}}}\left(1-\frac{1}{\sqrt{2}}\right) \)
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