If \( I_{n}=\int_{-n}^{n}\left(\{x+1\}\left\{x^{2}+2\right\}+\left\{x^{2}+3\right\}\left\{x^{3}+...

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If \( I_{n}=\int_{-n}^{n}\left(\{x+1\}\left\{x^{2}+2\right\}+\left\{x^{2}+3\right\}\left\{x^{3}+4\right\}\right) d x \), (where, \{\} denotes the fractional part), then \( I_{1} \) is equal to
\( (a)-\frac{1}{3} \)
(b) \( -\frac{2}{3} \)
(c) \( \frac{1}{3} \)
(d) \( \frac{2}{3} \)
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