What does it mean for an odd function to be odd about an end of an interval (at $x=L$, when the interval is $[0,L]$ or $[-L,L]$)?
E.g. the sine function is odd under reflection about $0$, but also about the end $L$ of the interval $[0,L]$.
What does this mean? Does it mean that it doesn't matter at which interval (containing $0$) one watches the sine, it will still be odd.
It means that $$f(L-x)=-f(L+x)$$