There is a part of this question I don't understand:

Eventually they ended up with:

$\displaystyle f(x)=\sum^{\infty}_{k=1} \frac{-2k \pi sinh 1 cos(k \pi)}{1+k^2 \pi^2} sin(k \pi x)$

So the part I don't understand right at the begining where they have:

$\displaystyle b_k= \int^1_{-1} sinh (x) sin (k \pi x) dx$

Should it not be $\displaystyle b_k= \frac{1}{2} \int^1_{-1} sinh (x) sin (k \pi x) dx$?

Because in my texbook $\displaystyle b_k$ is given by:

$\displaystyle b_k= \frac{1}{b-a} \int^b_a f(x)sin(kx) dx$

I'm very confused, can anyone help?