Integral of $$$y^{2}$$$

Apply the power rule $$$\int y^{n}\, dy = \frac{y^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=2$$$:

$${\color{red}{\int{y^{2} d y}}}={\color{red}{\frac{y^{1 + 2}}{1 + 2}}}={\color{red}{\left(\frac{y^{3}}{3}\right)}}$$

Therefore,

$$\int{y^{2} d y} = \frac{y^{3}}{3}$$

Add the constant of integration:

$$\int{y^{2} d y} = \frac{y^{3}}{3}+C$$

$$$\int y^{2}\, dy = \frac{y^{3}}{3} + C$$$A