By Parts and applyrule

Markiyan Hirnyk — Wed, 20 Feb 2013 02:08:36 Z

How about this?
>restart; infolevel[IntegrationTools] := 3:
>with(IntegrationTools): J := int(diff(y(x), x), x = 0 .. 2*Pi);
Definite Integration:   Integrating expression on x=0..2*Pi
Definite Integration:   Using the integrators [distribution, piecewise, series, o, polynomial, ln, lookup, cook, ratpoly, elliptic, elliptictrig, meijergspecial, improper, asymptotic, ftoc, ftocms, meijerg, contour]
LookUp Integrator:   unable to find the specified integral in the table
Definite Integration:   Returning integral unevaluated.


>Parts(J, 1);
Definite Integration:   Integrating expression on x=0..2*Pi
Definite Integration:   Using the integrators [distribution, piecewise, series, o, polynomial, ln, lookup, cook, ratpoly, elliptic, elliptictrig, meijergspecial, improper, asymptotic, ftoc, ftocms, meijerg, contour]
Definite Integration:   Method polynomial succeeded.
Definite Integration:   Finished sucessfully.
                        -y(0) + y(2 Pi)

>applyrule(y(x::numeric+2*Pi) = y(x), Parts(J, 1));
0

applyrule.mw See ?Parts and ?applyrule for more info.

MaplePrimes - answers and comments on Question, defining the periodicity of an unknown function

By Parts and applyrule