I am not sure how to proceed on the following problem:
Prove that there is a unique continuous fuction $f:[0,1]\to \mathbb{R}$, with the property that $f(x)=x+\int_0^1 \sin(2\pi (x-y))^2 f(y)dy$ for all $x\in [0,1]$.
I would appreciate just a hint :) Thanks in advance
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