Evaluating area under the curve
I have an area-under-the-curve problem. So, obviously, everyone knows that a definite integral is just a more accurate way of evaluating area under the curve, right?
So suppose you have your basic function f(x) = x^2. If you wanted to find the area under the curve from -3 to -2, you'd just integrate x^2.
Now, suppose you have the GRAPH for f(x), and you want to evaluate -3 to -2, but you don't know what the function is. Again pretty simple... you'd just evaluate from -3 to -2 with approximations as small rectangles/squares/etc.
My question is: what do you do if you have the graph of f(x), don't know what the function is, but you want to find the integral of f(x)^2dx? (Assume you don't know f(x) = x^2). What do you do in that case? Do you pick points (e.g. at -3, f(x) = 9, at -2, f(x) = 4, and then square these points? (I.e. f(-3)^2 = 81, f(-2)^2 = 16?) This might be accurate with a graph where f(x) = x^2, but what if f(x) = x^2 + 3? Can you apply the same methodology there?)
I'm really confused about this concept. Can anybody help me?