Given an initial value problem with separable differential equation $\displaystyle \frac{dy}{dx}=\frac{g(x)}{h(y)}$ and initial condition $\displaystyle (x_0,y_0)$ is it true that $\displaystyle \int_{y_0}^y h(t)dt=\int_{x_0}^x g(t)dt$ and is that the same as solving by using indefinite integrals and then using the initial condition to solve for the constant? If yes, how? I'm having trouble understanding. Thank you!