English: An example to demonstrate the construction of an integral using the Riemannian (blue) and Lebesgue (red) methods. For the Riemannian case, the domain is partitioned into eight intervals and bars are drawn to the function; the integral estimate is found by summing, over all bars, the product of the interval width and the bar height. For the Lebesgue integral, eight distinct target values in the range cause a partitioning of the domain into eight (not necessarily connected) subsets, with bars held beneath the function; the (pre-)integral is found by summing, over all domain subsets, the measure of each domain subset multiplied by its corresponding target value.