Inequalities Between Definite Integrals

$m_1 (b-a) \le \int_a^b f(x)\,\text{d}x$

If $m_1 < m_2 < m_3$, then $\int_a^b f(x)\,\text{d}x < m_3(b-a)$

$\min(\{m_1, m_2, m_3\}) \le \int_a^b f(x)\,\text{d}x$

$\min(\{m_1, m_2, m_3\})\cdot(b-a) \le \int_a^b f(x)\,\text{d}x$

$\int_a^b f(x)\,\text{d}x \le \max(\{m_1, m_2, m_3\}) \cdot (b-a)$