Question: Integral issue: How can I get the right value of an integral?

Hello, everyone!
Yesterday I accidentally rechecked the value of the integral of the function (below) and realized that it’s wrong:

f:= (x) -> (140.63530552419235473*x^4-681.04317103471061441*x^3+1204.2531184722204895*x^2-918.72829449327961838*x+254.16640660607969646)*x^10*(-5.985078986*10^(-7)*x^60+1.993612326*10^(-7)*x^61+5.369283226*10^(-8)*x^62-3.905639782*10^(-9)*x^64-1.659594038*10^(-8)*x^63+1.136103415*10^(-9)*x^65+2.247893270*10^(-10)*x^66-9.859204804*10^(-12)*x^68-6.233393896*10^(-11)*x^67+1.592005934*10^(-15)*x^73+2.636562187*10^(-12)*x^69+5.984365418*10^(-17)*x^74+3.098099702*10^(-13)*x^70-1.518364555*10^(-17)*x^75-6.215495764*10^(-15)*x^72-8.072161759*10^(-14)*x^71+7.108000000*10^(-7)-6.487695780*x^35-1.360148323*x^34+5.274954197*x^37+.278832666*x^36-.7198386404*x^43-3.348539406*x^39+.4203371703*x^38+.2531612707*x^45-.1973755246*x^44+1.711371118*x^41-.5547081746*x^40-0.7529286752e-1*x^47+0.7791628267e-1*x^46+.3904150312*x^42+0.1908735114e-1*x^49-0.2492657821e-1*x^48-0.4145806290e-2*x^51+0.6590414121e-2*x^50-0.4207722840e-4*x^56-0.1240685054e-3*x^55+0.7736126808e-3*x^53-0.1455570281e-2*x^52+0.1706676905e-4*x^57+0.5498382671e-5*x^58+0.2699386379e-3*x^54-0.2004264239e-5*x^59+.2715685673*x^10+.1111862378*x^8+.1883518910*x^9+0.2403811424e-1*x^6+0.5607230320e-1*x^7+0.8649081345e-2*x^5-3.880498062*x^31+5.968690982*x^33+2.038776931*x^32-1.725063618*x^30+1.669644062*x^29+.9016766288*x^28-.1370795088*x^25-.396947214*x^27-.348231765*x^26+.11698597*x^23+.2531405922*x^22+.1735045534*x^20-0.42936268e-1*x^19-0.39439553e-1*x^24-.3711884921*x^16+.28461699*x^21-.2677594262*x^18-.3961103119*x^17-.2103764104*x^15+0.113596644e-1*x^14+.205907773*x^13+.3148084900*x^12+.3274995670*x^11+0.5980983565e-3*x^3+0.1044830939e-3*x^2+0.2555141074e-2*x^4+0.1216249880e-4*x):

The notorious integral value:
int(f(x), x=0..2);
Maple 17 returned -2.552045317*10^6.  And what is more awkward that the result is changing over time. Despite the fact that some other computer algebra system tells me that the value must be about 6.0857912022, you can enjoy the plot of f(x):

How can we fix it?