What does Integral really mean?

Limit, derivative and integral are quick keywords for the calculus discipline, and generally listed in the respective order. In the most of the calculus courses, these concepts are taught as in the respective order as well.

On the other hand, chronological order is not really like that. I prefer to start teaching Calculus by integral. I know that it sounds interesting!

Following video is a short trailer of my introduction to calculus course.