(∫_(-1)^1) (1/(x^2)) \[DifferentialD]x

(∫_(-1)^1) 
            (1/((x^2) + (y^2))) \[DifferentialD]x

f[y_] = ((2 ArcCot[y])/y)
Limit[f[y], y -> 0]
g[y_] = (π/2) - 2 ArcCot[(1/y)];
h[y_] = y;
Limit[(∂_y) g[y]/(∂_y) h[y], 
      y -> 0]