Module[{length = 1, distance = 1},
 (*The exact expression before simplification*)
 N[\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(Pi\)]\(\((distance -
       length\ Sin[x])\) \[DifferentialD]x\)\)]/(Pi*distance);
 (*Simplified expression*)
 N[1 - 2 (length/distance)/Pi]
 ]