Calculate range of sin^2x-2sinx+5

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f (x) = ({sin}^{2} x - 2 sin x)

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

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

f (x)

sin 2 x + 2 sin x - cos x - 1 = 0

0 \leq x \leq 2 π

f (x) = \frac{2 {sin}^{2} x + 2 sin x + 3}{{sin}^{2} x + sin x + 1},

f

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