x(n):=sum(x[i],i,1,n)$

f(n):=sum(f[i](t),i,1,n)$

integrate(f(1),t,0,T);
integrate(f(10),t,0,T);
integrate(f(100),t,0,T);

integrate(f(1),t);
integrate(f(10),t);
integrate(f(100),t);

'integrate(sin(x),x,1,a(x)/b(x));

'integrate(sin(x),x,a(x)/b(x),1);