The range of the function $f : \mathbb R \to \mathbb R$, defined by $ f(x)=\frac{\sin\pi [x]}{s^{2}+5}$ is? 
Let $[x]$ denote the greatest integer less than or equal to $x$ for
  any real number $x$. The range of the function $f : R → R$, defined by
  $ f(x)=\frac{\sin\pi [x]}{s^{2}+5}$:
A.$ (−1, 1)$ 
B. $[−1, 1]$
C. $\{−1, 1\} $
D. $\{0\}$

The numerator oscillates between $-1$ and $1$, and the denominator can take any positive value. So the range is within $(-1,1)$ ??
I don't know how to find out if the function touches $-1$ and $1$?
Is the answer (A)$(-1,1)$ ??
Any help will be appreciated!

The answer is found by the questioner already: Since $[x]$ is always an integer, 
$$\sin \pi [x] = 0$$
for all $x\in \mathbb R$. Thus the range is $\{0\}$. 
