ClearAll;
f[x_]:= a + b x;
b = b/.Solve[Integrate[f[x],{x,0,5}]==1,b];
F[x_]:= Integrate[f[t],{t,0,x}];
prob = {1,2,4,6,10}/10;
squarederrors = Table[Simplify[(F[n]-prob[[n]])^2],{n,1,5}]
Apply[Plus,squarederrors]
Simplify[Apply[Plus,squarederrors]]

Factor[%-7/1300]