Fourier series for a function which changes

I don't know how to do this question I was given... I just need a pointer in the right direction, not a full solution please:

"A function is defined on 0<=x<=L by
f(x) = x for 0<=x<=L/2
       L-x for L/2<=x<=L

Find a sine Fourier series for f."

I know how to do this question, except for the fact that the function is actually two different things in the range 0 to L, which throws me off-track.

I need to find Bn, so would it work to find it for x as if that were the whole function with a range of 0 to L/2 , then add the Bn for L-x with a range of 0 to L, then take away the Bn for L-x in the range 0 to L/2?

I hope that made some sense... Or if you didn't understand it, just please post how you are meant to do this...

You don't have to do anything fancy.  f(L/2) = L/2 on both sides of the limit, so the thing's continuous (not a requirement, but it shows that the function's not as crazy as it could be)

The expansion coefficients are defined as integrals of some sort.  Just integrate over [0,L/2], then integrate over [L/2,L], and add (basically how you integrate over piecewise functions).

So what should I set L to be in Bn where you have the term sin (nxpi/L)? Should L just be equal to L in both cases, or equal to L/2 in both cases since they only go halfway, or something else?

Thanks.

So what should I set L to be in Bn where you have the term sin (nxpi/L)? Should L just be equal to L in both cases, or equal to L/2 in both cases since they only go halfway, or something else?

Thanks.