# How to calculate the area closed by a parabola and a line without calculus?

In order to simplify the problem, suppose we have a parabola $y=ax^2+bx+c$, here $a\neq0$, and a line $y=kx+d$, here $k\neq0$. We can assume that they will intersect at two different points. Thus, the $\Delta$ of the equation $ax^2+bx+c=kx+d$ will be greater than $0$($\Delta> 0$). Let $S$ be the area closed by them, it is clear that $S>0$.

Now I wonder how to calculate $S$ without calculus?

UPDATE:

I try to solve this problem without calculus in order to make my little brother who don't know about calculus understand it. You can solve it as long as you can make a junior student understand your solution. :)

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Which is your meaning of area? – Gastón Burrull Feb 16 '13 at 3:18
One can calculate without antiderivatives, in Riemann sum style, or in the Archimedean style, but limiting processes are inevitably involved. So in the wider sense of calculus, one cannot do it without calculus. – André Nicolas Feb 16 '13 at 3:26
The same happens when we try to calculate the area of a circle. – Gastón Burrull Feb 16 '13 at 3:29
@Gastón Burrull Edited. :) – felix34 Feb 16 '13 at 3:32
@Gastón Burrull I don't understand. We can calculate the area of a circle by using the formula $S=\pi r^{2}$, isn't it? – felix34 Feb 16 '13 at 3:46