$\int{a}{b}f(x)dx * \implies$
$\forall f: \mathbb{R} \to \mathbb{R}, \forall x \in \mathbb{R} \ f(x)=\lim_{a \to x}f(a) \\ \Rightarrow \forall y \in [\inf \{f(a), f(b) \}, \sup \{f(a), f(b) \}] \\ \Rightarrow \exists c \in (a, b) \ f(c)=y$
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