Arc Length In A Rectilinear Metric?

The Minkowski plane is defined by a rectilinear metric as follows:

For points (a,b)(a, b) and (m,n)(m, n), the distance between these points is


What is the length of the arc of f(x)=x2f(x)=x^2 from x=1x=-1 to x=1x=1 in this metric?

Notation: | \cdot | denotes the absolute value function.


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