# Arc Length In A Rectilinear Metric?

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

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

$d((a,b);(m,n))=|m-a|+|n-b|$

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

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

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