The value of $\int_0^1 \frac{d}{dx}\left[\tan^{-1}\left(\frac{1}{1-x+x^2}\right)\right]dx$ is (1) $\frac{\pi}{4}$ (2) $\tan^{-1}(2)$ (3) $\frac{\pi}{2} - \tan^{-1}(2)$ (4) $\frac{\pi}{4} - \tan^{-1}(2)$
The value of $\int_0^1 \frac{d}{dx}\left[\tan^{-1}\left(\frac{1}{1-x+x^2}\right)\right]dx$ is\\
(1) $\frac{\pi}{4}$\\
(2) $\tan^{-1}(2)$\\
(3) $\frac{\pi}{2} - \tan^{-1}(2)$\\
(4) $\frac{\pi}{4} - \tan^{-1}(2)$