Suppose \( f \) is continuous, \( f(0)=0, \mathrm{f}(1)=1, f^{\prime}(x)0 \) and \( \int_{0}^{1}...

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Suppose \( f \) is continuous, \( f(0)=0, \mathrm{f}(1)=1, f^{\prime}(x)0 \) and \( \int_{0}^{1} f(x) d x=\frac{1}{3} \). Find the value of the definite integral \( \int_{0}^{1} f^{-1}(y) d y \)
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