Problem with Justifying the Formula for First Order Seperable Differential Equations

Question

I am reading this text http://www.math-cs.gordon.edu/courses/ma225/handouts/sepvar.pdf to justify the method to solve first order seperable differentiable equations, where we are told first told that:

and then:

Now, while I can understand 1), I am struggling to understand how exactly the integral on the left hand side of 3) surmounts to $$\int n(y) dy$$ since $\frac{dy}{dx}$ can't be treated as a fraction.

Answer 1

you consider $y$ as a function of $x$ then $\frac{dy}{dx}= y'(x)$

to compute your integral just consider the change of variable formula:

$$\int n(y(x))y'(x)\, dx = \int n(y) dy $$