Psychophysics experiments showed that when multisensory stimulations arrive at nearly the same time, the time interval between them is perceived to be shortened. This is known as temporal integration. Meanwhile, neurophysics experiments showed that brain cells and nerve cells are able to anticipate future direction and location, therefore it is deduce that they encode predictive information. The capacity of continuous attractor neural networks (CANNs) in both temporal integration and prediction are considered. Furthermore, biological experiments showed that the coupling strengths of synapses between neurons can experience short-term changes depending on their firing histories, which is known as short-term synaptic plasticity (STP). We investigate how CANNs with STP causes signals to shift in time, in particular, how temporal integration behaves when network couplings and plasticities vary. We find that STP enables richer dynamics of integration, including order and time scale dependent integration. We also investigate how CANNs with STP track stimulus under stochastic processes. We find that STP allow the network to encode past or future information.