Compute the Laplace transform of $\displaystyle cos(at-b)$, where $\displaystyle a,b$ are real numbers.

I've tried this several times and I am ending up with an answer that I know is wrong. I seem to be making the same mistake over and over.

I set up the problem like this:

$\displaystyle \int{e^{-st}cos(at-b)}$

and then use integration by parts.

Judging by

WolframAlpha my answer should be

$\displaystyle \frac{s}{s^2+1}$

but I keep getting answers similar to this:

$\displaystyle \frac{-s}{s^2-a^2}e^{-st}[cos(at-b)+\frac{a}{s}sin(at-b)]$

Help would be greatly appreciated.