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 $