In the seventeenth century, Isaac Newton and Gottfried Wilhelm Leibniz independently discovered the idea that integration was a sort of opposite of differentiation (which they had just invented), which allowed mathematicians to calculate a broad class of integrals for the first time.
In the seventeenth century, Isaac Newton and Gottfried Wilhelm Leibniz independently discovered the idea that integration was roughly the inverse operation of differentiation, a way of measuring how quickly a function changed at any given point on the graph. This allowed mathematicians to calculate a broad class of integrals for the first time.