Upper and Lower Bounds of Integral/Corollary

Corollary to Upper and Lower Bounds of Integral
Let $f$ be a real function which is continuous on the closed interval $\closedint a b$.

Suppose that $\forall t \in \closedint a b: \size {\map f t} < \kappa$.

Then:
 * $\ds \forall \xi, x \in \closedint a b: \size {\int_x^\xi \map f t \rd t} < \kappa \size {x - \xi}$

Proof
Follows directly from Upper and Lower Bounds of Integral.