Range Of Function using differentiation

Write f(x) as
f(x)=\frac {\sin ^2x +\sin x -1}{\sin ^2 x- \sin x +2}=\frac {\sin ^2x -\sin x +2-3+2\sin x}{\sin ^2 x- \sin x +2}=1+\frac {2\sin x -3}{\sin ^2 x-\sin x +2}

isnt it better now ?

here
1 \leq \sin ^2 x-\sin x +2\leq 4,-5\leq 2\sin x -3 \leq -1

Here goes my answer........
tell me something is wrong........

sorry it is "tell me if something is wrong" in above post..............

dont u think u have made this ques too tuff ??
or have I made some mistake ...[3][3]

I ahve posted almost the full soln...[3]