Integration of a function defined by its graph, the union of semi-circles and a line segment I don't understand how to do this problem and I would someone to help me with it.Please step by step for me. I just started on integration so this problem is a bit too hard for me due to my lack of familiarity of using a graph for this sort of problems. 
I don't have a problem with part (a), but I don't know how to approach (b) and (c) as I wasn't really good at finding derivatives from graphs.

For (b) and (c):
Notice that at the end-points of each semi-circle, we have different slopes present. Part of the definition of a derivative is that the left and right limits must equal each other. If they do not equal one another, the derivative fails to exist at that point.
Therefore,
For (b) we must look at the graph of f. Notice that aren't any discontinuous points for f. Therefore, g' is continuous on that interval. 
For (c) we must look at the second derivative of g, or $f'$. We have that at $x=2$ and $x=6$ the derivative fails to exist because the left and right limits do no equal one another.
