F = (2/π) (ArcCos[x] - x*(Sqrt[1 - (x^2)]))

(∂_x) F

Plot[((4 (Sqrt[1 - (x^2)]))/π) , {x, -1, 1}]

Plot[F, {x, 0, 1}]

Sinc[t_] := Sin[t]/t

Stairs[
        t_, δ_] := (Sign[t]*Sign[t - 1  δ]*
              Sign[t + 1  δ]*Sign[t - 2  δ]*
              Sign[t + 2  δ]*Sign[t + 3  δ]*
              Sign[t - 3  δ] + 1)*
        UnitStep[4  δ - t]/2

Plot[Stairs[t, 1], {t, -5, 5}]

VisF[r_, δ_] := 
      NIntegrate[(((Sin[z]/z))^2)*
            Stairs[r - z, δ], {z, -10 δ, -0.000001}] + 
        NIntegrate[(((Sin[z]/z))^2)*Stairs[r - z, δ], {z, 
            0.000001, +10 δ}]

NIntegrate[(((Sin[z]/z))^2)*Stairs[1 - z, 1], {z, 
        1, +10}]

N[VisF[1, 1]]

Graph = Plot[VisF[t, 10], {t, -50, 60}]