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Compute an integral of (x+1)^2


    \[ \int_0^{-1} (x+1)^2 \, dx. \]

Since we computed \int_{-1}^0 (x+1)^2 \, dx in the previous exercise, we apply the theorem on expansion/contraction of the interval of integral (Theorem 1.19 in Apostol) with constant k=-1 to obtain,

    \[ \int_0^{-1} (x+1)^2 \, dx = - \int_{-1}^0 (x+1)^2 \, dx = -\frac{1}{3}. \]

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