I read in Calculus made easy book(Thompson) that Integration is adding up things( Summing of Infinite Infinitesimals. But is this correct? Because very few books give this definition whereas most books introduce integration as finding the area under Curve which is infact one of the applications of integration. Moreover I read on net that historically Integration was invented first and later the concept of derivative was developed.
Then how were Integral formulae found before Derivative concept was developed?