Calculating the space a complex shape takes is hard, but it's not hard to calculate the space of a rectangle, so why not use smaller and smaller rectangles.

Join me as I re-invent integrals without realizing what I am doing.

@olafurw at least re-invent the trapezoid rule like Mary Tai.
Tai's model - Wikipedia

Apparently, Calculus Was Invented In 1994

A paper written in 1994 purports to develop a 'mathematical model for the determination of total areas under curves.'

Forbes