  Using the fluid representation, we formulate the conditions for the
appearance of all four types finite-time future singularity in modified gravity
in accelerating FRW universe. It stressed that number of standard
quintessence/phantom DE theories (including scalar, fluid, DBI ones, etc)
brings the accelerating cosmology to future singularity precisely in the same
way as singular modified gravity DE. The viable non-singular modified gravity
unifying the early-time inflation with late-time acceleration is considered. It
is shown that adding such non-singular theory to another realistic singular
modified gravity which has the accelerating solution with future singularity
may cure the singularity of resulting combined model. This universal scenario
may be naturally applied to standard singular DE models as well as to
inflationary theories with initial singularity. This suggests the additional
fundamental reasoning for modification of General Relativity.
