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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-(tanx)xsgnx` be an even function for all `x in Rdot` Then the sum of all possible values of `a` is (where `[dot]a n d{dot}` denote greatest integer function and fractional part function, respectively). `(17)/6` (b) `(53)/6` (c) `(31)/3` (d) `(35)/3`

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