The value of \(\mathop \smallint \nolimits_{ - \pi /2}^{\pi /2} \frac{{dx}}{{\left[ x \right] + \left[ {{\rm{sin}}x} \right] + 4}}\), where [t] denotes the greatest integer less than or equal to t, is:

\(\frac{3}{{10}}\left( {4\pi - 3} \right)\)

\(\frac{1}{{12}}\left( {7\pi + 5} \right)\)

\(\frac{1}{{12}}\left( {7\pi - 5} \right)\)

\(\frac{3}{{20}}\left( {4\pi - 3} \right)\)

The value of \(\mathop \smallint \nolimits_{ - \pi /2}^{\pi /2} \frac{

1.	The value of \(\mathop \smallint \nolimits_{ - \pi /2}^{\pi /2} \frac{{dx}}{{\left[ x \right] + \left[ {{\rm{sin}}x} \right] + 4}}\), where [t] denotes the greatest integer less than or equal to t, is:
A.	\(\frac{1}{{12}}\left( {7\pi + 5} \right)\)
B.	\(\frac{1}{{12}}\left( {7\pi - 5} \right)\)
C.	\(\frac{3}{{20}}\left( {4\pi - 3} \right)\)
D.	\(\frac{3}{{10}}\left( {4\pi - 3} \right)\)
Answer» D. \(\frac{3}{{10}}\left( {4\pi - 3} \right)\)