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Induced emf ξ = - \frac{d \Phi}{dt},\ where\ \Phi=total\ magnetic\ Flux\ through\ the\ coil.

ξ = - d (8 t² + 3 t + 5) / d t
   = - 16 t + 3
   = -16 * 4 + 3 = - 61 Volts.

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so there is no role of the word fourth? i mean is there any difference between flux in FOUR seconds and flux at FOURTH second?
magnetic flux is an instantaneous quantity.. so you find it at t = 1, 2, 3, 3.4 sec.. like that... for finding emf induced, perhaps there is no meaningful use for adding flux over a duration of time..
instantaneous emf generated depends of rate of change of flux at a point of time only..