A common example to emphasize that it is not OK to bring absolute values inside the integral compares
abs( int( cos(n*x), x=0..Pi ) ) asuming n::integer
and
int( abs( cos(n*x) ), x=0..Pi ) assuming n::integer
Maple correctly formulates the first to 0. But the second expression gives it more trouble, returning two messages:
Warning, unable to determine if (1/2)*Pi*(1+2*_Z7)/n is between 0 and Pi; try to use assumptions or use the AllSolutions option
Warning, unable to determine if (1/2)*Pi*(1+2*_Z8)/n is between 0 and Pi; try to use assumptions or use the AllSolutions option