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Integral of tan^-1(x/(x^2 + 1)) + tan^-1((x^2 + 1)/x) from -1 to 3

The same question, asked 2 times: 11 May 2024 S1*, 21 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    11 May 2024 S1

    126
    ∫−13[cot⁡−1xx2+1+cot⁡−1x2+1x]dx=\int_{-1}^{3} \left[\cot^{-1}\frac{x}{x^2+1} + \cot^{-1}\frac{x^2+1}{x}\right]dx =

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  2. Question 2

    21 Apr 2025 S2

    107
    ∫−13(tan⁡−1(xx2+1)+tan⁡−1(x2+1x))dx=\int_{- 1}^{3} \left( \tan^{- 1}\left( \frac{x}{x^{2}+ 1} \right)+\tan^{- 1}\left( \frac{x^{2}+ 1}{x} \right) \right)dx=

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