How Should Integral Limits Change When Substituting in Trigonometric Functions?

[hancock.yang@]

Homework Statement

$$\int^{2\pi}_{0}cos^{2}(\theta)sin^{2}(\theta)cos(\theta)sin(\theta)d\theta$$
If I set x=cos$$^{2}$$($$\theta$$), the integral limit should be from 1 to 0 or need I break this integral into to 4 parts (i.e from 1 to 0 plus from 0 to 1 plus from 1 to 0 plus from 0 to 1)?

Homework Equations

The Attempt at a Solution

 

[jbunniii]

Do you know any trig identities that can be used to express

$$\cos(\theta) \sin(\theta)$$

in another way?