A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0)=f(2)=-1$, and $f(1)=1$. Which one of these statements must be true?

(A) There exists a $y$ in the interval $(0,1)$ such that $f(y)=f(y+1)$.

(B) For every $y$ in the interval $(0,1), f(y) = f(2−y)$.

(C) The maximum value of the function in the interval $(0,2)$ is $1$.

(D) There exists a $y$ in the interval $(0,1)$ such that $f(y) = − f(2−y)$.

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