What is \(\mathop \smallint \limits_{ - 1}^1 \left\{ {\frac{d}{{dx}}\left( {{{\tan }^{ - 1}}\frac{1}{x}} \right)} \right\}dx\) equal to?

What is \(\mathop \smallint \limits_{ - 1}^1 \left\{ {\frac{d}{{dx}}\l

1.	What is \(\mathop \smallint \limits_{ - 1}^1 \left\{ {\frac{d}{{dx}}\left( {{{\tan }^{ - 1}}\frac{1}{x}} \right)} \right\}dx\) equal to?
A.	0
B.	\( - \frac{\pi }{4}\)
C.	\( - \frac{\pi }{2}\)
D.	\(\frac{\pi }{2}\)
Answer» D. \(\frac{\pi }{2}\)