$$\int\_{0}^{2\pi}\int\_{1}^{e}\sin^{2009}(x)\frac{1}{y}dydx$$

In this question am I allowed to just pulled out the $2\pi$ right away from the integral from $0$ to $2\pi$? 

So that it becomes:

$$2\pi\int\_{1}^{e}\sin^{2009}(x)\frac{1}{y}dydx$$

---

$$\int\_{0}^{\frac{\pi}{2}}\int\_{0}^{e}\frac{\sin(y)}{x}dxdy$$

Could I do the same in this question by pulling out the $\pi/2$ right away for this question? If not, why can't I do it for this question? Can't I do it whenever there is no theta anywhere and the integral contains $\pi$?

Thank you