本题目来源于试卷: Integral Calculus，类别为 IB数学
[问答题]
1. Using the substitut+l.+v 3x k td)btyg3zwion v+ 8mcpw+5h+ 5.lcmngkvuaao/ *:bzi* 6 uocw $x=\cot \theta$ , show that $\int_{0}^{1} \frac{1}{\left(x^{2}+1\right)^{2}} \mathrm{~d} x=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \sin ^{2} \theta \mathrm{d} \theta$ .
2. Hence find the value of $\int_{0}^{1} \frac{1}{\left(x^{2}+1\right)^{2}} \mathrm{~d} x$ .
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