JEE Math Practice Question

Let f : R $$ \to $$ R be a function defined as $$f(x) = \left\{ \begin{matrix} {{\sin (a + 1)x + \sin 2x} \over {2x}},if\,x < 0 \hfill \\ b,\,if\,x\, = 0 \hfill \\ {{\sqrt {x + b{x^3}} - \sqrt x } \over {b{x^{5/2}}}},\,if\,x > 0 \hfill \\\end{matrix} \right.$$ If f is continuous at x = 0, then the value of a + b is equal to :

1. A.$$-$$3
2. B.$$-$$2
3. C.$$ - {5 \over 2}$$
4. D.$$ - {3 \over 2}$$