Integration is a function or operation in mathematics. It is the inverse function of the derivative function.
Integration is useful to find the area enclosed by the curve y = f(x), x axis and y axis. Integration is a very useful application in solving many differential equations.
In mechanical, chemical, aeronautical, civil, electrical engineering, pure sciences, economics etc., we find real life problems. To solve them, we first express relations among physical quantities using differential equations. They use derivatives. Then we find initial and final conditions. Integration is used to solve these equations.
Without integration, we cannot solve the consumption of fuel by a rocket, jet plane, amount of air resistance faced by a parachute, stress in structures. The electromagnetic waves are expressed in differential forms. we need integrals to solve them.