Solved
integral[x sqrt(1 + cos(2x)), 0, π / 2] ≒ 0.81
geogebra 5.0.472.0-d is -sqrt(2)
The same problem 
integral[x sqrt(1 + cos(2x)), 0, π / 2] ≒ 0.81
geogebra 5.0.472.0-d is -sqrt(2)
It's a bug both in v.5 and v.6 thank you. The result should be sqrt(2)
In CAS View of v.5 it gives a different answer. (the attached file is made with v.5)
The antiderivative of the integrand is
Thanks, fixed for v473
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