Question With Regards To Evaluating A Definite Integral When Evaluating the below definite integral $$\int_{0}^{\pi}(2\sin\theta + \cos3\theta)\,d\theta$$ 
I get this.$$\left [-2\cos\theta + \frac{\sin3\theta}{3}  \right ]_{0}^{\pi} $$
In the above expression i see that $-2$ is a constant which was taken outside the integral sign while performing integration. Now the question is should $-2$ be distributed throughout or does it only apply to $\cos\theta$? This is what i mean. Is it $$-2\left[\cos(\pi) + \frac{\sin3(\pi)}{3} - \left ( \cos(0) + \frac{\sin3(0)}{3} \right )  \right]?$$
Or the $-2$ stays only with $\cos\theta$?

Just think about the parity of the trigonometric functions and you're done
$$\int_{0}^{\pi}(2\sin\theta + \cos3\theta)\,d\theta=2\int_{0}^{\pi}\sin\theta\,d\theta=4$$
