Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = x^3 – 3x^2 + 2x and the x-axis?

Let . Suppose we define a new function that is transformed so that it is symmetric about the origin. This can be done with



Notice that is an odd function, since



So if is symmetric about the origin, this means must by symmetric about the point . This in turn means that the area between and the x-axis is the same from 0 to 1 as it is from 1 to 2. This means