The difference isn't in individual flaps, it's in the entire animation. There's only a difference in the first two flaps, after that they're identical.
The speeds are different - the right one smoothly goes from stationary to the target speed, while the left one appears to speed up and then slow down again. It's explained further down the article.
It's so handy to have functions that evaluate to either the derivative or the integral for a particular (version of a) shaping function like smoothstep.
Analytic integration has yielded some of the most stunning optimizations in graphics rendering! Replacing sample-the-hell-out-of-signal-and-integrate-the-samples with instead direct evaluation of an integral (or good-enough-standin-integral) function (where that itself can be known or derived) can yield many speedups and cool tricks!
