Find the area between the positive x axis and the line given by y=-(x^2)+2x

The first piece of understanding needed to answer this question is that integration can be used to find the area under a graph between two points. However, before we can integrate we must find the bounds between which we should integrate. With the aid of a graph we can see that those bounds are the two roots of the quadratic. By factorizing we can show that they are x=0 and x=2. Now we integrate:-x²+2x between the bounds x=0 and x=2, with respect to x. This gives us the final answer of 4/3.