The value of \( \int_{-1}^{1}\left\{x^{2}+x-3\right\} d x \), where \( \{\cdot\} \) denotes the ...

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The value of \( \int_{-1}^{1}\left\{x^{2}+x-3\right\} d x \), where \( \{\cdot\} \) denotes the fractional part of \( x \) , is equal to:
(a) \( \frac{1}{3}(1+3 \sqrt{5}) \)
(b) \( \frac{1}{6}(1+3 \sqrt{5}) \)
(c) \( \frac{1}{6}(3 \sqrt{5}-1) \)
(d) \( \frac{1}{3}(3 \sqrt{5}-1) \)
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