[kiba]

there is math, and then there is math. In Russia they have a saying "beat a rabbit long enough and it will eventually learn to take derivatives, but integrals are another matter".

A rabbit will be woefully unprepared to learn integrals if it forgot derivatives before it starts learning integral.

[jleader]

One moderately popular college calculus textbook (by Prof. Apostol of Caltech) introduces integrals before derivatives.