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Finding the area under a curve

The applet below computes the area of a figure made of rectangles which approximates the region under the given curve. This curve is the graph of a polynomial of degree three or less. The coefficients are listed in the boxes just above the graph. In the start-up exampel they are 0, 1, 0, 0, correspoding to the graph
y = x2,
a parabola. Graph
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Use the button "+" to increase the number of rectangles in the approximating figure, hence to increase its accuracy. As the number of rectangles increases, the' area of the figure gets closer and closer to the area under the curve. Thus the area under the curve is limit value of these approximations:

limit( An ) = A
where An is the are of the approximating figure and A is the area of the given figure.

Question: What is the area under the parabola?