## Calculus: Early Transcendentals 8th Edition

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.