Math Help - Finding the area under a curve

1. Finding the area under a curve

Can someone please explain the steps on how to find the area under the curve from x=0 to x=2.
When the function y= x/x^2+1.

2. $\frac{x}{x^2+1}$ or $\frac{x}{x^2}+1$?

3. (this one)

4. Let $u=x^2+1$

$du=2xdx$

$\frac {1}{2}du=xdx$

$\frac {1}{2} \int_0^2 \frac {du} {u}$

$\frac {1}{2} \bigg [\ln {x^2+1} \bigg ]_0^2$