Help with Piecewise function

[parisse]

Just define
f(t):=piecewise(t<0,-1, 1),
it's the same as your function on [-pi,pi] but in a much simpler form that int can handle.
Then (in Xcas), assume(n,integer); fourier_bn(f(t),t,2*pi,n,-pi) returns (-(-1)^n*2+2)/(n*pi)
As the warning explains, int can not handle piecewise condition that are not linear, in other words you must cut the definition interval in parts, each part being defined by one linear condition and implicit conditions deduced from the fact that previous case were not taken. For example, if a function is defined in [-inf,-2] as blabla, in [-2,0] as blurp, and in [0,inf] as gasp, do f(t):=piecewise(t<-2,blabla,t<0,blurp,gasp)