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Finding the length of a curve

The applet below computes the length of a broken-line approximation to a 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 segments in the broken-line approximation, hence to increase its accuracy. As the number of segments increases, the' length of the broken-line curve gets closer and closer to the arc length of the curve. Thus the arc length is limit value of these approximations:

lim( Ln ) = L
where Ln is the length of the n-segment approximation and L is the length of the curve.

Question: What is the arc length of the given parabola?