question_answer

If for a real number y, [y] is the greatest integer less than or equal to y, then the value of the integral \[\int\limits_{\pi /2}^{3\pi /2}{[2\sin x]\,\,dx}\] is

A)  \[-\pi \]                         

B)  \[0\]

C)  \[-\frac{\pi }{2}\]          

D)  \[\frac{\pi }{2}\]

E)  None of these