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Thanks for reporting ! However, it is fixed in recent beta releases of Sage, see:

sage: integral(sqrt(1-cos(x)), x, 0, pi)
2^(3/2)

http://sagecell.sagemath.org/?z=eJzLzCtJTS9KzNEoLiwq0TDUTc4v1qjQ1NRRqNBRMNBRKMjUBADPVgqU&lang=sage

Thanks for reporting ! However, it reporting, this is fixed in recent beta releases of Sage, see:now trac ticket 24587 !

sage: integral(sqrt(1-cos(x)), x, 0, pi)
2^(3/2)