The curve `y=1/(1+x^2)` lies entirely above the `x`-axis for all values of `x`, so to find the area we can simply integrate. (If part of the curve was below the `x`-axis, we would need to split it into different portions and take absolute values.)

`"Area"=int_0^2(dx)/(1+x^2)`

`=[tan^-1x]_0^2`

`=[tan^-1 2-tan^-1 0]`

`=1.1071\ "units"^2`