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

1
0
2
\( - \frac{\pi }{4}\)
3
\( - \frac{\pi }{2}\)
4
\(\frac{\pi }{2}\)

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