Integral of -5y^2 dx

1. The integral of a constant times a function is the constant times the integral of the function:

   $$\int \left(- 5 y^{2}\right)\, dy = - 5 \int y^{2}\, dy$$

   1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$:

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

   So, the result is: $- \frac{5 y^{3}}{3}$

2. Add the constant of integration:

   $$- \frac{5 y^{3}}{3}+ \mathrm{constant}$$

The answer is:

$$- \frac{5 y^{3}}{3}+ \mathrm{constant}$$