We sketch the curve first to see what is going on.

This is the curve `y=sin(x)`:

π 1 -1 x y
`(3pi)/2`

The shaded region represents the integral we need to find.

We need to split the integration into 2 portions because one part of the curve is above the `x`-axis (the part from `0` to `pi`), and the rest of it is below the `x`-axis (the part from `pi` to `(3pi)/2`, and we'll need to take the absolute value).

`"Area" =int_0^pi sin x\ dx+|int_pi^(3pi//2)sin x\ dx|`

`=[-cos x]_0^pi+` `|-cos x|_pi^(3pi//2)`

`=[-cos pi-(-cos 0)]+` `|-cos (3pi)/2-(-cos pi)|`

`=[1+1]+|0-1|`

`=3\ "units"^2`