Reference: Improper Integrals, R. C. Daileda, http://ramanujan.math.trinity.edu/rdaileda/teach/m4342f10/improper_integrals.pdf
install_github("YasuakiHonda","euler-maclaurin-sum","master")$
asdf_load_source("euler-maclaurin-sum")$
[assume(M>N),assume(N>=1),assume(s>1),assume(x>=N)];
INT0:integrate(periodic_bernpoly(x,n)/x^s,x,N,M);
(INT1:integrate(abs(periodic_bernpoly(x,n)/x^s),x,N,M))>=abs(INT0);
assume(C>part(INT1,1,1));
substpart(C,INT1,1,1)>=INT1;
%,nouns,expand;
map(lambda([F],limit(limit(F,M,inf),N,inf)),%);
rhs(%)=0;