Domain of the function \( f(x)=\frac{\sin [x-1]}{[x-1][x+2]} \) where \( [x] \) denotes the grea...

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Domain of the function \( f(x)=\frac{\sin [x-1]}{[x-1][x+2]} \) where \( [x] \) denotes the greatest integer function less than \( x \), is
(a) All real \( x \)
(b) \( [-2,-1) \)
(c) \( R-[-2,-1) \cup[1,2) \)
(d) \( R-[-2,2] \)
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