Question: two problems about user defined periodic function

restart;
#plot(exp('frem'(x+1,3)-1),x=-5..5,discont);
int(exp('frem'(x+1,3)-1),x=-5..5);
Error, (in int) wrong number (or type) of arguments: invalid options or option values passed to exact integration
evalf(Int(exp('frem'(x+1,3)-1),x=-5..5));
Error, (in evalf/int) when calling 'frem'. Received: 'invalid input: frem received x+1, which is not valid for its 1st argument, x'
sol1:=dsolve({diff(x(t), t)=eval(piecewise(0 <= t and t < 10/3, 60, 10/3 <= t and t < 13/3, 0),t='frem'(t,13/3)),x(0)=0},numeric,output=listprocedure);
sol2:=dsolve({diff(y(t),t)=eval(piecewise(0 <= t and t < 4, 50, 4 <= t and t < 5, 0),t='frem'(t,5)),y(0)=0},numeric,output=listprocedure);
#two commands above are well,but the below is not well.
sol:=dsolve({diff(x(t), t)=eval(piecewise(0 <= t and t < 10/3, 60, 10/3 <= t and t < 13/3, 0),t='frem'(t,13/3)),diff(y(t),t)=eval(piecewise(0 <= t and t < 4, 50, 4 <= t and t < 5, 0),t='frem'(t,5)),x(0)=0,y(0)=0},numeric,output=listprocedure);
Error, (in signum) invalid input: frem received t, which is not valid for its 1st argument, x
plots:-odeplot(sol,[[t,x(t)],[t,y(t),color=blue]],t=0..50,gridlines=true,thickness=2);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution.

any advice is appreciated.