Let f:[0,∞)→R a non-decreasing function. Then show this inequality holds for all x,y,z such that 0≤x<y<z.
\begin{align*} & (z-x)\int_{y}^{z}f(u)\,\mathrm{du}\ge (z-y)\int_{x}^{z}f(u)\,\mathrm{du} \end{align*} calculusintegrationinequalitiesrearrangement inequalityreal analysisIntegral inequality