There, had to make a post to see which one showed up. My avatar is a chalkboard with an apple. Written on the chalkboard is the indefinite integral of e^x dx. I'm a math teacher among other things. I could probably edit my avatar to show a goat chewing on the edge of the chalkboard, but that would only perpetuate the myth that goats eat anything. In reality, they're picky eaters (it's just that they'll eat a couple of things you wouldn't expect them to eat.)
Anyway, to explain further, the integral is the symbol for the anti-derivative. But, I'm getting ahead of myself. Suppose we wanted to find the area under some continuous smooth curve f(x) over some interval, say, 0 to x*. Obviously, the area should depend on the value of x* that we choose, thus we can say that F(x*), the area under the curve from 0 to x* is a function of x. Now, I don't know how to find the area under the curve, but it might be surprising to discover that I can take the derivative of it. Using the definition of the derivative, the limit as h approach zero of f(x+h)-f(x) all over h, we can describe this limit geometrically... (to be continued if I ever get that bored.)