This work investigates the controllability and stability properties of nonlinear piecewise dynamical systems subject to integral boundary conditions studied in arbitrary time domains. The study employs powerful mathematical ideas like fixed point theorems, Gramian-type matrices and the unified approach given by the theory of time scales. This unified approach provides results applicable seamlessly in various settings of continuous-time systems, discrete-time systems, and systems with hybrid behavior of both. This paper expands existing findings in the literature, providing a more complete view. To show the application of the theoretical results, a detailed example is presented and supported by numerical simulations to confirm the efficiency of the proposed methods.