Answer
True.
Work Step by Step
An increasing function is such that
$x_{1} > x_{2} \Rightarrow$ $f(x_{1}) > f(x_{2})$
On the interval [a,b], any x that is not a is greater than a,
so it follows that
$f(x) > f(a)$
for every $x\in(a,b].$
(There is no x in the interval with f(x) that is less than f(a))
f(a) is the minimum value of f in [a,b].
The statement is true.
