Answer
TRUE
Work Step by Step
We know that
$\int _{a}^{b}f(x) dx=f(b)-f(a)$ [Second Fundamental Theorem of Calculus]
Rewrite as
$\int _{a}^{b}f(x) dx=f(b)-f(a)+f(c)-f(c)$
$\int _{a}^{b}f(x) dx=f(c)-f(a)+f(b)-f(c)$
$\int _{a}^{b}f(x) dx=\int _{a}^{c}f(x) dx+\int _{c}^{b}f(x) dx$
Hence proved.
Therefore, the given statement is true.