We evaluate the polarizabilities of the 5p(1/2), 6s, 6p(1/2), and 6p(3/2) states of In using two high-precision relativistic methods: the linearized coupled-cluster approach, where single, double, and partial triple excitations of the Dirac-Fock wave function are included to all orders of perturbation theory, and an approach that combines the configuration interaction and the coupled-cluster method. An extensive comparison of the accuracy of these methods is carried out. The uncertainties of all recommended values are evaluated. Our result for the 6s-5p(1/2) Stark shift is in excellent agreement with a recent measurement [Ranjit et al., Phys. Rev. A 87, 032506 (2013)]. Combining our calculation with this precision measurement allows us to infer the values of the 6p(1/2) and 6p(3/2) lifetimes in In with 0.8% accuracy. Our predictions for the 6p(3/2) scalar and tensor polarizabilities may be combined with the future measurement of the 6s-6p(3/2) Stark shift to accurately determine the 5d(j)-6p(j ) matrix elements. DOI: 10.1103/PhysRevA.87.032513