[Rick]

Sorry, was away.

For your first question, assuming the area under the graph between x=b and x=m is equal to the area under the graph between x=m and x=a, and assuming you know the values of a and b, you could actually find the integral of y=f(x), and then substitute in the values and equate them.

i.e.
let g(x) be the function of the integral of f(x)
thus g(b) - g(m) = g(m) - g(a)

Then rearrange and solve for m. If you come out with a polynomial, you can find the discriminant and check if it's more than or equal to 0. If not, there's no point solving for m since there's no (real) solutions.

As for your second question, I actually don't know what you mean. Maybe clarify it a little?

God I looked at this thread and I didn't have a clue as to what I was talking about, my notation is just shocking.

I found this which was essentially what I was looking for, I could barely understand what I was talking about in that post don't worry.