The most important people for developing integrals:

Archimedes

In ancient Greece, Archimedes (287-212 BC) was the first person who found formulas for the surface areas and volumes of solids such as the sphere, the cone, and the paraboloid. His method of integration was remarkably modern considering that he did not have algebra, the function concept, or even the decimal representation of numbers.

Kepler

  

 

Johannes Kepler (1571-1630, Germany) developed methods to

calculate surface areas and volumes of solids. 

 The most important person in developping integrals

Leibniz

Newton

Leibniz (1646-1716) and Newton (1642-1727) independently discovered calculus. Their key idea was that differentiation and integration undo each other. They develop the general rules for integrals. Using this symbolic connection, they were able to solve an enormous number of important problems in mathematics, physics, and astronomy.