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This is definitely a bug, which seems to originate from the name psi for one of the two functions: it is confused with Maxima's special function psi, see http://maxima.sourceforge.net/docs/manual/maxima_15.html#Item_003a-psi

If you replace psi by another name, everything works:

sage: f = function('f')
sage: g = function('g')
sage: y = var('y')
sage: integrate(g(x-y)*f(y), y)
integrate(f(y)*g(x - y), y)

This is definitely a bug, which seems to originate from the name psi for one of the two functions: it is confused with Maxima's special function psi, see http://maxima.sourceforge.net/docs/manual/maxima_15.html#Item_003a-psi

If you replace psi by another name, everything works:

sage: f = function('f')
sage: g = function('g')
sage: y = var('y')
sage: integrate(g(x-y)*f(y), y)
integrate(f(y)*g(x - y), y)

UPDATE (13 March 2019): the bug is now tracked via the ticket #27475.