[Maxima] Integrating function with abs or max

[Ray Tice]

How do I reformulate functions that use abs or max so that maxima can integrate them?
  For example, integrate(abs(x), x, -1, 1)  won't evaluate, but both of these will:
    integrate(abs(x), x, -1, 0)
    integrate(abs(x), x,  0, 1)
   
  Am I missing out on a better way to describe equations to maxima?
  Maybe I'm missing a flag to subdivide problems? (I am rather a newbie in Maxima)
   
  Indefinite integration fares no better even in the simple case.
   
  Of course, the above answer is easy to construct, even for high school students,
  It's less easy for a human to do it flawlessy for even slightly more complidated problems:
     f(x) := max(1-abs(x), 0)
     integrate(f(x)*f(x-a), x)
   
  Thanks, Ray

 
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