Riemann Integration partitions the domain ($x$-axis) into small intervals and sums the area of rectangles. Lebesgue Integration partitions the range ($y$-axis) into slices and sums the measure of the sets mapped to those values.
Henri Lebesgue: "I have to pay a certain sum... Riemann counts the coins one by one... I stack coins of same value and count each stack." Instructions: Switch between modes. Use the slider to increase partitions. Hover over the graph to highlight specific slices.
Hover over the plot to see details.