pie/2 to pie the value of greates interger function of 2 sinx is zero so intergal value under this region is zero .

now pie to 7pie/6 the value is -1 so intergal one . so that value is -pie/6.

now 7pie/6 to 3pie/2 the value os step function is -2 so intergal of -2  so value is -2pie/3 so total value is -5pie/6

 

 

 

 

 

if iam wrong plz correct me.