Mad Man's Mountain

Every day, Naranath starts from the bottom of a valley and pushes his boulder all the way up to the summit of a mountain. He then lets it roll all the way back down the mountain and laughs thunderously.

$f(x) = \cos^5(x) + 1, x \in [-\pi, \pi]$

...represents the height of the mountain at a given point. How far does the boulder roll every day?

Details and assumptions:

• The boulder stops as soon as it hits the bottom of the valley; it doesn't roll any further.
• Round to the hundredth's place.