Straight Line Segment is Shortest Path between Two Points/Lemma 2

Lemma to Straight Line Segment is Shortest Path between Two Points

Let:

$\forall x \in \closedint a b: \map f x = \map g x$

Then:

$\ds \int_a^b \map f x \rd x = \int_a^b \map g x \rd x$

Proof

Follows directly from the definition of the definite integral.

$\blacksquare$