The problem is that hkti is an unevaluated integrate expression, where t appears both in the expression to be integrated and the integration variable. The (t=something) substitution blindly substitutes something to t in both...
• hkti(t=T) will become integrate(sin(A*cos(2*pi*T/T) + kx), T) (i.e. integrate(sin(A*cos(2*pi*1) + kx), T), then integrate(sin(A+kx), T), i.e. trivially T*sin(A+kx)). Probably not what you mean...
• hkti(t=0)will become integrate(sin(A*cos(2*pi*0/T) + kx), 0), which is nonsense (there is no such thing as an integration with respect to a constant...).