Integral given to SEEMOUS 2011.Need help!

For a given integer $ n\ge1 $,let f:[0,1]--->R be a non-decresing function.Prove that:
$ \int^1_0 f(x)\,dx\le (n+1)\int^1_0 x^nf(x)\,dx $.
Find all non-decreasing continuous functions for wich equality holds.

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