Let \( f(x) \) be a continuous function given by \( \mathrm{P} \) \...

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Let \( f(x) \) be a continuous function given by
\( \mathrm{P} \) \( f(x)=\left\{\begin{array}{cl}2 x, & |x| \leq 1 \\ x^{2}+a x+b, & |x|1\end{array}\right. \), then
The area of the region in the third quadrant bounded by the curves \( x=-2 y^{2} \) and \( y=f(x) \) lying on the left of the line \( 8 x+1=0 \) is
(1) sq. units
(2) \( \frac{257}{192} \) sq. units
(3) \( \frac{257}{96} \) sq. units
(4) \( \frac{289}{192} \) sq. units
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