E is open interval in \mathbb{R}, a, b be two points in E and a \mathbb{R} is continuous such that f(x

[answerhappygod]

E is open interval in \mathbb{R}, a, b be two points in E and
a<b. Assume f: E -> \mathbb{R} is continuous such that f(x)
\geq 0, and there exist a point c \in (a, b) such that f(c) \neq
0.
a) Prove \int_{a}^{b} f > 0
b) Prove there exist a point n in (a,b) such
that \int_{a}^{n} f = 3 * \int_{n}^{b} f