We expose simple and practical relations between the integrated four- and five-point one-loop amplitudes of N >= 4 supergravity and the corresponding (super-) Yang-Mills amplitudes. The link between the amplitudes is simply understood using the recently uncovered duality between color and kinematics that leads to a double-copy structure for gravity. These examples provide additional direct confirmations of the duality and double-copy properties at loop level for a sample of different theories.