What is a 'basic region' in calculus?

What is a 'basic region' in calculus? My friend told me that a basic region is defined as a connected set in which the total boundary consists of a finite number of continuous curve of the form $y=f(x)$ or of the form $x=g(y)$. Is the above definition correct?

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"A basic region is a connected set in which the total boundary consists of a ﬁnite number of continuous arcs of the form $x_2=\phi(x_1),x_1=\psi(x_2)$."