You cannot ignore the absolute value.
Break up the integral into the parts where sin x is positive and negative and flip the negative part over.
Then you can integrate.
This means that $\displaystyle |sin(x)|= - sin(x)$
soo then is it
abs sinx= sinx if x=> 3pi/2
=-sinx if x< 3pi/2
so then integral from 0 to pi sinx+ integral from pi to 3pi/2 -sinx
which is then [-cosx]+ [cosx]
[(-cos0)-(-cospi)]+ [(cospi)-(cos3pi/2)]
[-1-(1)] + [-1-(-1/2)]
-2-1/2
=-2.5??