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Let f(x)=([a]^2-5[a]+4)x^3-(6{a}^2-5{a}+...

Let `f(x)=([a]^2-5[a]+4)x^3-(6{a}^2-5{a}+1)x-(tan)x sin x` be an even function for all `x in R` Then the sum of all possible values of `a` (where `[.] and {.}` denot greatest integer function and fractional part function,respectively). (a) `17/6` (b) `53/6` (c) `31/6` (d) `35/3`

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