You need to explain in your posts what you know how to do and what you don't. This will help us help you better.
So for (a) you need to find the derivative of your equation and construct a tangent line formula. This is fairly standard, so I'll assume you know about how to do this unless you tell me otherwise.
Once you find this line, you need to use integration to find the area of the shaded region. First, what is the region of integration? Put another way, what are the bounds of integration? When you have an area between two curves, call it h(x), you write it in terms of the two equations. So is the region made by C-C' or C'-C?