to a): The rotation volume with the x-axis as axis of rotation is calculated by:

In your case a = 0 and b = 2

To determine the integral use integration by substitution with

which will give

After some simplifications you should come out with

to b) Are you asked to calculate the area between the x-axis and the graph of the function or do you want to evaluate the integral.

In the first case you have to split the domain into 3 parts.

In the second case you have to split the domain into 2 parts.

Draw a sketch of the graph and you'll see why these preparations are necessary.