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Question:

A. $\frac{\pi}{3}$

B. $\frac{2 \pi}{3}$

C. $\frac{\pi}{6}$

D. $\frac{\pi}{12}$

Solution:

$\int \frac{d x}{1+x^{2}}=\tan ^{-1} x=\mathrm{F}(x)$

By second fundamental theorem of calculus, we obtain

$=\tan ^{-1} \sqrt{3}-\tan ^{-1} 1$

$=\frac{\pi}{3}-\frac{\pi}{4}$

$=\frac{\pi}{12}$

Hence, the correct answer is D.