# Domain and Range!

Calculus Level 4

$\large \dfrac{\sin^2 x + \sin x -1}{\sin^2x - \sin x + 2}$

For real $$x$$, the range of the function above can be expressed as $$\left [ \dfrac{A-B\sqrt C}D , \dfrac EF \right ]$$, where $$A,B,C,D,E$$ are all positive integers with $$A,D$$ and $$E,F$$ coprime pairs, and $$C$$ square-free.

Find the value of $$A+B+C+D+E+F$$.

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