What does taking the integral of x(t) yield? I'm very inquisitive and far ahead of my school math, but i have yet to understand what the result is.
It yields many many many many many many things.
One of them is the average value. If you want to know how big $x(t)$ is on average for $t$ between $t=a$ and $t=b$, find the integral of $x(t)$ from $t=a$ to $t=b$, and divide by $b-a$.