eqns={y''[t]+y[t]==3a Sin[y[t]],y[0]==y'[0]==1};
pfun=ParametricNDSolveValue[eqns,(∫_0^5)y[s]\[DifferentialD]s,{t,0,5},{a}];

Plot[pfun[a],{a,-4,4},AxesLabel->{a,(∫_0^5)y[s,a]\[DifferentialD]s},ImageSize->Medium]

outFun[f_]:=ParametricNDSolveValue[eqns,f,{t,0,5},{a}];
dataRow[f_]:=Plot[outFun[f][pa],{pa,-3,3},AxesLabel->{a,f},ImageSize->Small];
outputs={{y[1]+y[2],(∫_0^5)y[s]\[DifferentialD]s},{y'[3],y[Abs[a]]}};

Grid[Map[dataRow,outputs,{2}],Frame->All,ItemStyle->{Automatic},Spacings->{1.5,1.5}]