The second half of calculus looks for the distance traveled even when the speed is changing. Finding this “integral” is the opposite of finding the derivative. Professor Strang explains how the integral adds up little pieces to recover the total distance.

I know the speed at each moment of my trip, so how far did I go?

Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here.

Subtitles are provided through the generous assistance of Jimmy Ren.