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a = 0;
(*beginning point*)
b = 3; (*ending point*)
f[x_] := (1 - x)^2;(*function*)

points[x_] := 
  Table[{i, f[i]}, {i, a, 
    b, (b - a)/
     x}]; (*generates a list of the points for the line segments*)
distance[x_] := 
  Sum[Sqrt[((b - a)/x)^2 + (f[i] - f[i - (b - a)/x])^2], {i, 
    a + (b - a)/x, 
    b, (b - a)/
     x}];(*evaluates the approximate length of the line segment*)