#4201 integrate fails in a sign when working with trigonometric functions under the root

[Ilya Dikarev]

 integrate(sqrt(1-sin(t)^2)*cos(t), t, %pi, %pi/2);

should give %pi/4, but gives -%pi/4. I think the problem is, then in the integration domain sqrt(1-sin²t) = |cos t| = -cos t.

But maxima for some reason works with |cos t| = cos t

[Ilya Dikarev]

The same problem appears if we change it to:

integrate(sqrt(1-sin(t)^2)*cos(t), t, %pi/2, %pi);

is should give -%pi/4, but returns %pi/4

Maxima 5.43.2