Please help me to find what's wrong with the answer to the calculation of:
$$\int_{1}^{1+2 \pi} (\cos x) e^{-(\sin x)^2} dx$$
Let $t=\sin x$
$dt = \cos x dx$
$x=1 \implies t=\sin 1$,
$x=1+2\pi \implies t=\sin 1$
So the integral is
$$\int_{\sin 1}^{\sin 1}e^{-t^2}dt=0$$