ABSTRACT
The integral was first introduced by Isaac Newton (1643-1727) and Gottfried Wilhelm Leibniz (1646-1716) for functions defined on an interval. In its first 150 years of existence, the definition of the integral was loose and imprecise (measured with the standard of today’s mathematics), and the precise definition that you (probably) have learned in your elementary calculus course is due to Bernard Riemann (1826-1866). It was extended to arbitrary measures in the beginning of this century by mathematicians such as E. Borel, H. Lebesgue, C. Carathéodory and many others.
