The driving force of overall development comes from the demand in practical application. In practice, some unknowns can sometimes be roughly estimated, but with the development of science and technology, it is often necessary to know the exact values.

If the area or volume of simple geometry is needed, the known formula can be applied. For example, the volume of a rectangular swimming pool can be calculated by length x width x height.

The concept of Lebesgue integral is defined on the concept of measure. Measurement is the generalization of measuring length and area in daily concepts, and it is defined in an axiomatic way. Riemann integral can actually be regarded as a series of rectangles covering the graph below the function curve as much as possible. The area of each rectangle is the length times the width, or the product of the lengths of two intervals.

Measure defines the concept of similar length for a set in a more general space, so that the area of a graph can be "measured" under a more irregular function curve, thus defining an integral.