signal processing – Linearity and stationarity of a system with integral

How can I demonstrate the linearity and the stationarity of system with integrals? For example I have this signal $ y(t)= int_{t}^{t-T} x(tau ) dtau $ and I know from theory that’s a filter so I should have both linearity and stationarity but I didn’t obtain this. For stationarity I first apply a delay on the input ( x(t) = x(t-t0) ) of the system and after on the output , ( t= t-t0 ).