Now I am providing the complete solution to this problem :
For ease of understansing , let us change the variable x to C
Now consider a triangle whose sides are a, b ( fixed )(a>b) and their intermediate angle C is variable .
Now it is clear that the Dr. of the given integrand =

so the integral now becomes

Now applying Sine rule , we know that

again we have that
dC = - dA -dB
Now let us imagine what would be the limits of A & B as C varies from 0 to
( with a>b ) .
when C->0 , A->
& B->0
again when C->
, A->0 & B->0 { Draw a figure with a>b & observe the above result yourself !! }
so the integral becomes now

The last integral is clearly zero !!
So the ultimate integral is

but a is constant ; so the result is
=
( hence proved )