# Inequality in integration

Let $$f:(0,infty)rightarrowmathbb R$$ be a non-decreasing continuous function. Show that the inequality $$qquad$$
$$(z-x)intlimits_{y}^{z}f(u)dugeq (z-x)intlimits_{x}^{z}f(u)du$$ holds for any $$0leq xlt y lt z$$