f[t_]:=5+Sin[t]+Cos[3t];
Plot[f[t],{t,0,2π},PlotRange->{All,{3,7}}]

tValues=Range[0,2*π,0.1];
fValues=f/@tValues;

ListPlot[Transpose[{tValues,fValues}],PlotRange->{All,{3,7}}]

EasyFcn[{t1_,f1_},{t2_,f2_}]:=(f1+f2)/2*(t2-t1);
Sum[
EasyFcn[{tValues[[i]],fValues[[i]]},{tValues[[i+1]],fValues[[i+1]]}],
{i,1,Length[tValues]-1}
]

Length[tValues]

tValues

tValues[[4]]