The first should be pretty simple. But I'm just checking to see if I made any careless mistakes. My answer is -x/4+1/2.

The second question seems tricky. I thought about doing it the manual way ie.e differentiating and integrating y to find it's first derivative, then divide it by 2, where I'll obtain g(x) and I' d then integrate g(x) with limits 2 and 1 respectively. Is there an easier way? Or is my idea above flawed? I don't have the answer with me at the moment.

The third should be similar. But if I integrate the first derivative to obtain it's original equation, I'd have to add a constant value to the equation. Unless I don't need to do so, I should be able to obtain y=14x, where I integrate it with limits 3 and 0. Is that correct?

Regarding the fourth question, I'm not sure on how to proceed. Does the first part of the question refer to 0.5(3+8)(6)?