JEE Math Practice Question

Let f : R $$ \to $$ R be defined as $$f(x) = \left\{ \begin{matrix} 2\sin \left( { - {{\pi x} \over 2}} \right),if\,x < - 1 \hfill \\ |a{x^2} + x + b|,\,if - 1 \le x \le 1 \hfill \\ \sin (\pi x),\,if\,x > 1 \hfill \\\end{matrix} \right.$$ If f(x) is continuous on R, then a + b equals :

1. A.$$-$$3
2. B.3
3. C.$$-$$1
4. D.1