Someone has a proof that the anti-derivative of a piecewise function does not exist



I found this on the web.

http://www.mathhelpforum.com/math-help/f6/showing-there-no-anti-derivative-piecewise-function-154607.html

Curiously the proof is wrong.

display2d:false;
false

load(pw)$

pw([minf,x,0,1,inf],x);
(signum(x)+1)/2+x*(1-signum(x))/2

deltaint(%,x);
-x^2*(2*unit_step(x)-1)/4+x*(2*unit_step(x)-1)/2+x^2/4+x/2

diff(%,x);
-x*(2*unit_step(x)-1)/2+(2*unit_step(x)-1)/2+x/2+1/2

pwsimp(%,x,'list);
[minf,x,0,0,0,1,inf]