# 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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