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Is there an easy way to get the area under a curve given these restrictions:

1. The curve is described by second degree polynomial

2. The area we are interested in is the complete range between the zero's on the x-axis

In other words, what is the area under the curve between the zero's of a(x-b)(x-c)

It seems to be that this should be narrow enough to be calculable without doing series and integrals and whatnot (calculus, I don't know the exact approach yet), but I can't seem to find anything that fits.

So, is there a nice solution to this?