Semi urgent - Laplace Transform

Hi all,

I'll state the question, then explain my thinking.

Evaluate $\displaystyle \int_0^{\inf} [ H(t - \frac{\pi}{4}) - H(t)] \cos{2t}e^{-st} dt$ where $\displaystyle s > 0 $

Ok, I know the heaviside function limits the range between 0 and $\displaystyle \frac{\pi}{4}$.

I also know that the laplace transform of $\displaystyle \cos{2t}$ is $\displaystyle \frac{s}{s^2 + 4}$

What I don't know is how I'm meant to effectively combine these properties together to correctly evaluate the integral.

Any help would be greatly appreciated.