Interval type for Fourier Analysis on $L^2( [-\pi,\pi) ) $

Question

Why is it that in many texts the natural domain of choice is $L^2 ( [- \pi, \pi) ) $ as opposed to $L^2 ( [- \pi, \pi] ) $? I would to think of the space $L^2 ( [- \pi, \pi] ) $ as the completion of $C_{c}( [- \pi, \pi] )$, so that I can use the fact that trig functions have compact support on the interval $[- \pi,\pi]$, but many books use $[- \pi, \pi)$.