Let f: R → R be defined as f(x)= {2 sin (-(π x)/2), if x<-1; | a x^2+x+ b |, if -1 ≤ x ≤ 1; sin (π x), if x>1} If f(x) is continuous on R, then a + b…

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $$f(x)= \begin{cases}2 \sin \left(-\frac{\pi x}{2}\right), & \text { if } x<-1 \\ \left|\mathrm{a} x^2+x+\mathrm{b}\right|, & \text { if }-1 \leq x \leq 1 \\ \sin (\pi x), & \text { if } x>1\end{cases} $$ If $\displaystyle f(x)$ is continuous on $\displaystyle \mathbf{R}$, then $\displaystyle \mathrm{a}+\mathrm{b}$ equals :