f[x_] := 5.6489268459732293*10^3*x^0 + 1.5840388646726304*10^4*x^1 +
1.8411479431773834*10^4*x^2 + 1.1346125105186486*10^4*x^3 +
3.9100547469412686*10^3*x^4 + 7.1432694208139674*10^2*x^5 +
5.4027518253964281*10^1*x^6
Plot[f[x], {x, -2.99, -1.7}, PlotRange -> {Automatic, {0, 6}},
Filling -> Bottom, PlotLabels -> {"f[x]"}]
AREA = NIntegrate[f[x], {x, -2.99, -1.7}]
(* 5.79828 *)