Quiet@Remove["Global`*"];
SetDirectory[NotebookDirectory[]];
$HistoryLength=3;

data1=Import["Kveten2018_celkovy_prutok.xls"];

data2=data1[[1,2;;]];
Δt=5/60.;(*hod*)
data3=Last/@data2;
ListPlot[data3,PlotRange->All];
nDat=Length[data3];

data4=Drop[data3,-1];
Length[data4]

intSimson=((Δt)/3)*Total[Partition[data4,3,2]/.{a_,b_,c_}:>a+4b+c];
konecek=Δt*Mean[Take[data3,-2]];
Print["integral celkem= ",intCelkem=intSimson+konecek];
Print["simpson= ",intSimson,"  konecek= ",konecek]

vahy1=Join[{1},Riffle[Table[4,{i,(Length[data4])/2}],2],{1}];

vahy=Join[{1},{4,2}&/@Range[(Length[data4])/2-1]//Flatten,{4,1}];
{a,b,c}.{1,2,4}

intSimson=((Δt)/3)*(vahy.data4);
konecek=Δt*Mean[Take[data3,-2]];
Print["integral celkem= ",intCelkem=intSimson+konecek];
Print["simpson= ",intSimson,"  konecek= ",konecek]

intSimson=((Δt)/3)*Plus@@({1,4,1}.#&/@Partition[data4,3,2]);
konecek=Δt*Mean[Take[data3,-2]];
Print["integral celkem= ",intCelkem=intSimson+konecek]

listCasu=Δt*Range[0,nDat-1];
data2D=Thread[{listCasu,data3}];
intData=Interpolation[data2D,InterpolationOrder->2];
tmax=Last[listCasu];
NIntegrate[intData[t],{t,0,tmax}]

sol=NDSolve[{e'[t]==intData[t],e[0]==0},e,{t,0,tmax},MaxSteps->(10^6)][[1]]
e[tmax]/.sol

Range[10]
Partition[%,3,2]
%/.{a_,b_,c_}:>a+4b+c
Total[%]