Off[GraphicsArray::obs]

ClearAll[f];
f[t_]:=t+(7/10)*(t^2)+(7/10)*(t^3);
t1=1;
t2=2;
plr={Automatic,{-0.1,f[t2]+0.5}};
pl1=Plot[f[t],{t,t1,t2},AxesLabel->{"t","f[t]"},PlotRange->plr,PlotStyle->Thick];

intZcelaSpravne=Integrate[f[t],{t,t1,t2}];
numerickySpravne=NIntegrate[f[t],{t,t1,t2}];

n0=5;
nmax=20;
Manipulate[

Δt=((t2-t1)/(n-1));
tecka=Range[t1,t2,Δt];
efka=f@tecka;
obdelnikyDolni=Graphics[{Brown,Opacity[0.2],Rectangle[{#,0},{#+Δt,f[#]}]}]&/@Take[tecka,n-1];
lines=Graphics[{GrayLevel[0],Opacity[1],PointSize[0.008],Arrow[{{#,0},{#,f[#]}}]}]&/@tecka;
bodyt=Graphics[{Hue[0],Opacity[1],Thickness[0.005],Point[{#,0}]}]&/@tecka;
plDolni=Show[pl1,obdelnikyDolni,lines,bodyt,PlotRange->plr];
obdelnikyHorni=Graphics[{Orange,Opacity[0.2],Rectangle[{#,0},{#+Δt,f[#+Δt]}]}]&/@Take[tecka,n-1];
obdelnikyStred=Graphics[{Blue,Opacity[0.2],Rectangle[{#,0},{#+Δt,f[#+0.5Δt]}]}]&/@Take[tecka,n-1];
plHorni=Show[pl1,obdelnikyHorni,lines,bodyt];
bodyStred=Graphics[{Hue[0],Opacity[1],Thickness[0.005],Point[{#,0}]}]&/@Range[t1+0.5Δt,t2-0.5Δt,Δt];
linesStred=Graphics[{GrayLevel[0],Opacity[1],PointSize[0.008],Arrow[{{#+0.5Δt,0},{#+0.5Δt,f[#+0.5Δt]}}]}]&/@tecka;
plStred=Show[pl1,obdelnikyStred,linesStred,bodyStred];
intDolni=Δt*Plus@@(N[f/@Range[t1,t2-Δt,Δt]]);
intHorni=Δt*Plus@@(N[f/@Range[t1+Δt,t2,Δt]]);
intStred=Δt*Plus@@(N[f/@Range[t1+0.5Δt,t2-0.5Δt,Δt]]);
vysSred=Show[plStred,PlotLabel->StringJoin["intStred= ",ToString[intStred],",  δ= ",ToString[((100(intStred-numerickySpravne))/numerickySpravne)],"  %"]];
vysDolni=Show[plDolni,PlotLabel->StringJoin["intDolni= ",ToString[intDolni],",  δ= ",ToString[((100(intDolni-numerickySpravne))/numerickySpravne)],"  %"]];
vysHorni=Show[plHorni,PlotLabel->StringJoin["intHorni= ",ToString[intHorni],",  δ= ",ToString[((100(intHorni-numerickySpravne))/numerickySpravne)],"  %"]];
vysArray=GraphicsArray[{{vysDolni},{vysHorni},{vysSred}}];
{vysDolni,vysHorni,vysSred,vysArray}[[i]]
,{{n,n0},n0,nmax,1},{{i,1,"pripad"},Range[4]},ControlPlacement->{Top,Top}]