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?
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. :)