Integration of Function

Calculus Level 3

\(y=f(x)\) is a continuous odd function in \(\mathbb{R}\) defined as follows:\[f(x)=\frac{\pi}{2}\int_{1}^{x+1}f(t)dt.\] Given that \(f(1)=1,\) evaluate the following integral:\[\pi^2\int_{0}^{1}xf(x+1)dx.\]

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