Find the number of integers in the range of the real-valued function $y=\sqrt{\log_2 (\sin x)}.$
For the function to be defined, we must have $\log_2 (\sin x) \ge 0,$ so $\sin x \ge 1.$  But since $\sin x \le 1,$ the only possible value of $\sin x$ is 1.  Then $y = \sqrt{\log_2 1} = 0,$ and the range contains only $\boxed{1}$ integer.