If \( \int_{0}^{1} e^{-x^{2}} d x=a \), then \( \int_{0}^{1} x^{2} e^{-x^{2}} d x \) is equal to...

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If \( \int_{0}^{1} e^{-x^{2}} d x=a \), then \( \int_{0}^{1} x^{2} e^{-x^{2}} d x \) is equal to
(a) \( \frac{1}{2 e}(e a-1) \)
(b) \( \frac{1}{2 e}(e a+1) \)
(c) \( \frac{1}{e}(e a-1) \)
(d) \( \frac{1}{e}(e a+1) \)
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