result = 1/T * int(x^2 * tau, tau, t-T/2, t+T/2)
result = 
tau should be chosen from user
No, that is inconsistent with you integrating with respect to tau (the dtau in your expression) . The variable of integration cannot have a value chosen by the user.
Perhaps t is being chosen by the user?
x=Discrete data, with dt=0.005
Does that imply that x is a function of t? The same t that is being used in the bounds? If so then you should not be doing an integral, and should instead be doing a numeric summation or perhaps a trapz over the x that are in the range t-T/2 to t+T/2
