Find the area bounded by y=x3−x and y=x2+x

y=x3−x=x(x−1)(x+1) is a cubic polynomial  function intersecting the x -axis at (−1,0),(0,0),(1,0) . y=x2+x=x(x+1) is a quadratic function which is concave  upward and intersect x -axis at (−1,0)(0,0) .  The graphs of curves are as shown in following figure.  From the figure,   Requiredarea =∫−10 x3−x−x2+xdx+∫02 x2+x−x3−xdx =∫−10 x3−x2−2xdx+∫02 x2+2x−x3dx =x44−x33−x2−10+x33+x2−x4402 =0−14+13−1+83+4−4 =3712 sq. units