If \( f(x) \) is a continuous function for all real values of \( x \) and satisfies \( \int_{n}^...

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If \( f(x) \) is a continuous function for all real values of \( x \) and satisfies \( \int_{n}^{n+1} f(x) d x=\frac{n^{2}}{2} \forall n \in I \), then \( \int_{-3}^{5} f(|x|) d x \) is equal to :
(a) \( \frac{19}{2} \)
(b) \( \frac{35}{2} \)
(c) \( \frac{17}{2} \)
(d) \( \frac{37}{2} \)
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