The value of the integral \( I=\int_{0}^{1} x(1-x)^{n} d x \) is eq...

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The value of the integral \( I=\int_{0}^{1} x(1-x)^{n} d x \) is equal to
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(1) \( \frac{1}{n+1} \)
(2) \( \frac{1}{n+2} \)
(3) \( \frac{1}{n+1}-\frac{1}{n+2} \)
(4) \( \frac{1}{n+1}+\frac{1}{n+2} \)
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