In this talk, we will consider several regularity results for viscosity solutions of fully nonlinear nonlocal equations. For fully nonlinear second order partial differential equations, the regularity theory made a remarkable progress in the late 20th century, and especially the following three important estimates were established: Schauder estimate, Cordes--Nirenberg estimate and Calder\'on--Zygmund estimate. In the case of nonlocal equations, the analogs of the first two estimates have already been proved: Schauder estimates by Serra (2015) and Jin--Xiong (2015) independently and Cordes--Nirenberg estimate Caffarelli--Silvestre (2011), whereas Calderón--Zygmund estimate for integral equations is our new result. The key is to analyze Riesz potentials of solutions for integral equations, which are also solutions of certain second-order partial differential equations.