Basics of integration

I am finding the topic of integration quite difficult, but particularly when I get questions asking for area under a function!
I was just wondering if anyone could help me with this question so I become more confident in the subject :

"Calculate the area enclosed by the curve y = (x -1)^3 and the straight line y = (x -1). Make a sketch, labelling the points at which the curve intersects the straight line."


Thank you!!!

I assume you know what the graph x^3 looks like? So if we add in (x-1) in that would move it one unit to the right. Draw a sketch of that finding out where the graph crosses the x axis setting y=0. Draw the line y=x-1. Post a picture once you have sketched it we should be able to help you from there.

Area between $y=(x-1)^3$ and the x axis is $\int(x-1)^3 dx$ and that between line $y=x-1$ and x axis is $\int(x-1)dx$ so area between them is $\int[(x-1)^3-(x-1)]dx$ evaluated between the x coordinates of the points of intersection.