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If \(I\left(x\right)=\int {e}^{{\sin }^{2}x}(\cos x\sin 2x-\sin x)dx\) and \(I(0)=1\), then \(I\left(\frac{\pi }{3}\righ…

Q1

If \(I\left(x\right)=\int {e}^{{\sin }^{2}x}(\cos x\sin 2x-\sin x)dx\) and \(I(0)=1\), then \(I\left(\frac{\pi }{3}\right)\) is equal to

a

\(-\frac{1}{2}{e}^{\frac{3}{4}}\)

b

\({e}^{\frac{3}{4}}\)

c

\(\frac{1}{2}{e}^{\frac{3}{4}}\)

d

\(-{e}^{\frac{3}{4}}\)

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