why gives a wrong result?

edit

I know the track. And the question has been placed bearing in mind that the error is already known.

But the true question is: does anyone know what is the problem in the pipe between SageMath and Maxima that produces this type of "obviously" incorrect results? What are the types of integrals that are known to suffer from this problem?

With this information I can try to avoid the problem (in fact, teach my students). Not fixing the problem (I do not know enough about the involved algorithms/programation) but retouching the math to get a more "friendly" (or hard enough) expression to work.

Here's another one that doesn't integrate correctly:

integrate(sqrt(1+cos(x)^2),x,0,pi)

This doesn't work either:

integrate(sqrt(1+cos(x)^2),x,0,pi,algorithm='sympy')