Using a graph, it can be shown that the approximate $x$-coordinates of the points of intersection of the two curves $y=x^4$ and $y=3x-x^3$ are $x = 0$ and $x \approx 1.17.$ Use this information to approximate the area of the region bounded by these curves.

Make sure your answer (based on the estimates given above) is correct to two decimal places.

Area =