Continuous function/Integral equality/Point equality/Exercise

Let

$f,g\colon [a,b]\longrightarrow \mathbb {R}$

be two continuous functions such that

${}\int _{a}^{b}f(x)dx=\int _{a}^{b}g(x)dx\,.$

Prove that there exists ${}c\in [a,b]$ such that

${}f(c)=g(c)$.

Create a solution