Integral of $$$y$$$

Apply the power rule $$$\int y^{n}\, dy = \frac{y^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=1$$$:

$${\color{red}{\int{y d y}}}={\color{red}{\frac{y^{1 + 1}}{1 + 1}}}={\color{red}{\left(\frac{y^{2}}{2}\right)}}$$

Therefore,

$$\int{y d y} = \frac{y^{2}}{2}$$

Add the constant of integration:

$$\int{y d y} = \frac{y^{2}}{2}+C$$

$$$\int y\, dy = \frac{y^{2}}{2} + C$$$A