Integrating function with abs or max

You can also do something like:

(%i1) matchdeclare(x,true,a,true,b,true);
(%o1) done
(%i2) tellsimp('integrate(abs(x),x), x * abs(x) / 2)$
(%i3) tellsimp('integrate(abs(x),x,a,b), b * abs(b) / 2 - a * abs(a)/2)$
(%i4) integrate(abs(x),x);
(%o4) (x*abs(x))/2
(%i5) integrate(abs(x),x,-6,10);
(%o5) 68


With some work, maybe it would be possible to get  simple things like

(%i6) integrate(abs(x-2),x);
(%o6) integrate(abs(x-2),x)

to work too. And .....

Barton