Proving an integral identity with swapped variables

[RSGuy]

Can anyone prove the following theorem?
$$\int_{0}^{z} \frac{dy}{dx} dz = \int_{0}^{y} \frac{dz}{dx} dy$$

 

[mathman]

What is the relationship between y and z and how are they dependent on x?

 

[Tide]

Can anyone prove the following theorem?
$$\int_{0}^{z} \frac{dy}{dx} dz = \int_{0}^{y} \frac{dz}{dx} dy$$

HINT: $dz = \frac {dz}{dy} dy$