Answer
$f(x) = tan~x,~~~$ $~~~0 \leq x \leq \frac{\pi}{4}$
Work Step by Step
For each $x_i$, such that $1 \leq i \leq n$, note that $x_i = (i\frac{\pi/4}{n}) = \frac{i\pi}{4n}$
$\Delta x = \frac{\pi/4}{n} = \frac{\pi}{4n}$
We can express the area under the graph as a limit:
$A = \lim\limits_{n \to \infty} [f(x_1)\Delta x+f(x_2)\Delta x+...+f(x_n)\Delta x]$
$A = \lim\limits_{n \to \infty} \sum_{i=1}^{n}~\frac{\pi}{4n}~tan~\frac{i\pi}{4n}$
This limit is equal to the area under the graph:
$f(x) = tan~x,~~~$ $~~~0 \leq x \leq \frac{\pi}{4}$
