Integral and Area of a section bounded by a function. I'm having a really hard time grasping the concept of an integral/area of a region bounded a function.
Let's use $x^3$ as our sample function.
I understand the concept is to create an infinite number of infinitely small rectangles, calculate and sum their area. Using the formula
$$\text{Area}=\lim_{n\to\infty}\sum_{i=1}^n f(C_i)\Delta x=\lim_{n\to\infty}\sum_{i=1}^n\left(\frac{i}n\right)^3\left(\frac1n\right)$$
I understand that $n$ is to represent the number of rectangles, $\Delta x$ is the change in the $x$ values, and that we are summing the series, but I still don't understand what $i$ and $f(C_i)$ do. Is $f(C_i)$ just the value of the function at that point, giving us area? 
Sorry to bother you with a homework question. I know how annoying that can be.
P.S. Is there a correct way to enter formulas?

So, $f(C_i)$ is the value of $f$ at $C_i$, but more importantly it is the height of the specific rectangle being used in the approximation.  Then $i$ is just the interval which is the base of the rectangle.  As $|C_{i+1}-C_i|\rightarrow 0$, this sum becomes the area under the curve.
