Let \( f: R \rightarrow R \) be defined as \( f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\...

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Let \( f: R \rightarrow R \) be defined as
\( f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\pi x}{2}\right), & \text { if } x-1 \\ \left|a x^{2}+x+b\right|, & \text { if }-1 \leq x \leq 1 \\ \sin (\pi x) & \text { if } x1\end{array}\right. \)
If \( f(x) \) is continuous on \( R \), then \( a+b \) equals
(a) -3
(b) -1
(c) 3
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