Find the area of the region bounded by the curves $y=x^{2}$ and $y=x^{3}$.

Step 1 ：Set the two equations equal to each other to find the points of intersection: \(x^{2} = x^{3}\).

Step 2 ：Solve for x to find the points of intersection. The solutions are x = 0 and x = 1.

Step 3 ：Calculate the area between the two curves by integrating the absolute difference of the two functions over the interval of intersection. The integral is represented as \(\int_{0}^{1} |x^{3} - x^{2}| dx\).

Step 4 ：Evaluate the integral to find the numerical value of the area. The area is approximately 0.0833333333333333.

Step 5 ：Final Answer: The area of the region bounded by the curves \(y=x^{2}\) and \(y=x^{3}\) is \(\boxed{0.0833}\).