If area bounded by \( y=g(x), x \)-axis and the lines \( x=-2 \), \( x=3 \), where \[ g(x)=\left...

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If area bounded by \( y=g(x), x \)-axis and the lines \( x=-2 \), \( x=3 \), where
\[
g(x)=\left\{\begin{array}{l}
\max \{f(t) ;-2 \leq t \leq x\},-2 \leq x0 \\
\min \{f(t) ; 0 \leq t \leq x\}, 0 \leq x3
\end{array}\right.
\]
and \( f(x)=x^{2}-|x| \), is equal to \( A \), then correct statement is
(a) \( A \) is \( \frac{113}{24} \) sq. units
(b) \( g^{\prime}(x)=0 \forall x \in(-2,0) \)
(c) \( g^{\prime}(x)=0 \forall x \in(0,3) \)
(d) \( g(x) \) is even function
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