# 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 \(A+B+C+D+E+F\).