The area bounded by the curve y=x[x]; x-axis and the ordinates x=1, x=-1 is given by-
I just difficult to compute the area here because the drawing facility is not available in this platform but I can suggest you how to approach this type of problem
first draw the graph of function given on the xy plane and then start with the boundary condition given and then mark the shaded area with pencil and then you can easily computer with little bit of mensuration knowledge the area of shaded region this is the required answer