The one-loop effective action for non-minimal scalar modified gravity on de Sitter background with a constant
scalar field is found. The corresponding induced cosmological constant is evaluated. It is shown that quantum effects in
non-minimal modified gravity may induce an early-time de Sitter universe even in the situation when such solution does
not occur on the classical level. Classical reconstruction of the theory is presented in such a way that the resulting theory
has a cosmological solution unifying early-time inflation with late-time acceleration.