Answer
$ \int_0^1 [(x-1)^3 - (x-1) ] dx + \int_1^2 [ (x-1) - (x-1)^3 ] dx $
Work Step by Step
Set up to find the area bounded by the two functions
Because $y_2$ changes from the lower function to the upper function over two intervals, two integral need to be used.
Set up the integration by using the form $\int (f(x) - g(x) )$ where f(x)>g(x),
For the first interval, $y_1$ is the upper function and $y_2$ is lower,
Then on the second interval $y_1$ changes to the lower and $y_2$ changes to the upper.
$ \int_0^1 [(x-1)^3 - (x-1) ] dx + \int_1^2 [ (x-1) - (x-1)^3 ] dx $
