We can define the Fourier sine transform as $$F[f(x)](s)=\int_{-\infty}^{+\infty}f(x) \sin (sx) dx\:.$$
Now the inverse sine transform is $$f(x) =\int_{-\infty}^{+\infty}F(s) \sin (sx) ds\:.$$
I have used this formula to evaluate the value of $f(x)$ but I can't.
The problem that you ask has no answer because $\sqrt{s}$ is imaginary for for negtaive $s$. The answer that I think you are after is problem 1) part (b) of this homework set. I think that there is enough explained there for you to finish it off yourself.