The FitzHugh-Nagumo (FN) system is a prototypical model for simulating different modes of neuronal spiking activity. We propose a simple formulation of the FN model to simulate the phenomenon of synaptic integration, i.e., the processing of synaptic action potentials to generate postsynaptic spikes. We further show how the model can be used to probe the dynamical properties of postsynaptic spike trains, such as their responses to noise. We consider the phenomena of stochastic and coherence resonance to illustrate the same.