int Sin(x)

\int Sin(x) = -Cos(x)

\int Sin(x) = \frac {e^{ix}  –  e^{-ix}}{2i}

\int \frac{e^{ix}}{2i}  – \int \frac{e^{-ix}}{2i}

\frac{e^{ix}}{2i^{2}}  –  ( – \frac {e^{-ix}}{2i^{2}} )

\frac{e^{ix}}{2i^{2}}  + \frac {e^{-ix}}{2i^{2}}

i^{2} = -1

– \frac{e^{ix}}{2}  –  \frac{e^{-ix}}{2}

Factor out -1

– (\frac{e^{ix}  +  e^{-ix}}{2}) = -Cos(x)