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We investigate the first-passage problem where a diffusive searcher stochastically resets to a fixed position at a constant rate in a bounded domain. We put forward an analytical framework for this problem where the resetting rate r, the resetting position x r, the initial position x 0, the domain size L, and the particle's diffusion constant D are independent variables. From this we obtain analytical expressions for the mean-first passage time, survival probability and the first-passage time density in Laplace space in terms of the above independent variables, and closed forms in time-domain expression in some cases. For the first-passage time distributions their full-time profiles in time-domain are numerically obtained and validated by Monte Carlo simulations. We show that for the general resetting condition the first-passage process has rich nontrivial features as it combines effects from resetting and the finiteness of the …