Upper Darboux integral
= Upper Darboux integral
{title2=$\overline{\int_a^b}f=\inf_PU(f,P)$}
The upper Darboux integral of a bounded real function on a closed interval is the <infimum> of its <upper Darboux sums> over all <partitions of an interval>. Refinement decreases an <upper Darboux sum>, and the function is <Riemann integrable> precisely when this infimum agrees with its <lower Darboux integral>.