Integral of $$$\sin{\left(\phi \right)}$$$

Find $$$\int \sin{\left(\phi \right)}\, d\phi$$$.

The integral of the sine is $$$\int{\sin{\left(\phi \right)} d \phi} = - \cos{\left(\phi \right)}$$$:

$${\color{red}{\int{\sin{\left(\phi \right)} d \phi}}} = {\color{red}{\left(- \cos{\left(\phi \right)}\right)}}$$

Therefore,

$$\int{\sin{\left(\phi \right)} d \phi} = - \cos{\left(\phi \right)}$$

Add the constant of integration:

$$\int{\sin{\left(\phi \right)} d \phi} = - \cos{\left(\phi \right)}+C$$

$$$\int \sin{\left(\phi \right)}\, d\phi = - \cos{\left(\phi \right)} + C$$$A