Let f : R → R be a function defined as
\(f(x)=
\begin{cases}
\frac{sin(a+1)x+sin\,2x}{2x}&, if\,x<0\\
\,\,\,\,\,\,\,\,\,\,\,\,b&,if\,x=0\\
\frac{\sqrt{x+bx^3}-\sqrt x}{bx^{5/2}}&,if\,x>0
\end{cases}
\)
If f is continuous at x = 0, then the value of a + b is equal to:
(1) \(-\frac 52\)
(2) -2
(3) -3
(4) \(-\frac 32\)