So, I read this post on the the area of the sine curve some time ago and in the bottom was this equally amazing comment :

Diameter of the circle/ The distance covered along the x axis starting from and ending up at .

And therefore by the same logic, it is extremely intuitive to see why:

Because if a dude starts at and ends at , the effective distance that he covers is 0.

If you still have trouble understanding, follow the blue point in the above gif and hopefully things become clearer.