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