Inflationary slow-roll dynamics in the Einstein gravity with non-minimal scalar-curvature coupling (known as Higgs inflation) is shown to be equivalent to that in the f(R) modified gravity theory (known as Starobinsky inflation). I give a proof of the correspondence and extend it to N=1 supergravity. The non-minimal coupling in supergravity is reformulated in terms of the standard (minimal) N=1 matter-coupled supergravity by using curved superspace. The equivalence relation between the supergravity theory with the nonminimal scalar-curvature coupling and the recently constructed F(R) supergravity (which is the N=1 locally supersymmetric extension of f(R) gravity) during slow-roll inflation is established in the manifestly supersymmetric way. The equivalence does not hold after inflation during reheating. The main reference is arXiv:1201.2239.