Evaluate the following integrals:

Let $I=\int e^{-2 x} \sin x d x$

We know that, $\int \mathrm{e}^{\operatorname{ax}} \sin b x d x=\frac{e^{\operatorname{ax}}}{a^{2}+b^{2}}\{a \sin b x-b \cos b x\}+c$

$=\frac{e^{-2 x}}{5}\{-2 \sin x-\cos x\}+c$