I have this function:
\begin{equation*} f(x)=% \begin{cases} 1 &x\in\left[ -\pi,-\pi/2\right[ \\ -1 &x\in\left[ -\pi/2,0\right[\\ 1 & x\in\left[ 0,\pi/2\right[ \\ -1 & x\in\left[ \pi/2,\pi\right]\\ \end{cases} \end{equation*}
First I thought that it was odd, but then I realized that $f(0) = 1 \neq - f(0) = -1$ was true. Does it matter when you calculate an integral and want to use the property of an odd function? For instance can I still deduce that:
\begin{equation*} \int_{-a}^{a} f(x) dx = 0 \end{equation*}
?