campo=VectorPlot[{1,t^2-1},{t,-4,4},{y,-4,4},VectorScale->{0.02,0.02,None},Axes->True,AxesLabel->{"t","y"}]

VectorPlot[{1,t^2-1},{t,-4,4},{y,-4,4},VectorScale->{0.02,0.02,None},Axes->True,AxesLabel->{"t","y"},StreamPoints->10]

DSolve[{y'[t]==t^2-1,y[0]==2},y[t],t]

f[t_]:=(1/3) (6-3 t+(t^3))

solucion=Plot[f[t],{t,-4,4},PlotStyle->{Thick,Red}]

punto=Graphics[{PointSize[Large],Point[{0,2}]}];

Show[campo,solucion,punto]