Average $y$ from a range of $x$ in a parabola Given a parabolic/quadratic formula such as $ax^2 + bx + c =y$, how do I get the average value of $y$ given a range of $x$ ($x_{min}$ to $x_{max}$).
Real world example: if my formula represents the trajectory arc of a thrown object under the force of gravity, where $x$ is time and $y$ is height, I'm looking for the object's average height within a timespan.

The average of a function $f(x)$ in the interval $a$ to $b$ is given as
$$\frac{1}{b-a} \int_a^b f(x) dx$$
