Function of a given derivative (calc I)

[Swerting]

I was given a graph of a derivative, f'(x), and I have determined that it's formula is:
$$f'(x)=-abs(x-1)+1$$
It wants to know what the function f(x) is, as in the formula given that f(1)=0. I would be able to do this except I can't figure out what the function would BASICALLY look like! what would the function f(x) look like if its derivative is f'(x)=abs(x)? I know that the value of the derivative increases until x=1, where it then decreases, so it has somewhat of a mound shape, and the point (1,1) exists on the function of the derivative, so would it be a peak? i know it can't be an asymptote, but is a peak some kind of exception where the derivative ressembles the function itself?

I just need a push in the right direction of what the original function may look like.

 

[statdad]

Note that

$$|x| = \begin{cases}<br /> \hphantom{-}x, & \text{ if } x \ge 0\\<br /> -x, & \text{ if } x < 0<br /> \end{cases}$$