If f and g are integrable on [a, b] and f(x) ≥ g(x) for all x in... | Agrigyan

Comparison Property of Definite Integrals (Monotonicity):
If $f$ and $g$ are integrable on $[a, b]$ with $a \le b$, and if $f(x) \ge g(x)$ for all $x \in [a, b]$, then:
$f(x) - g(x) \ge 0 \implies \int_a^b [f(x) - g(x)] dx \ge 0 \implies \int_a^b f(x) dx \ge \int_a^b g(x) dx$.
This is the fundamental monotonicity property of Riemann integration.

Option breakdown:

• They can be equal if $f(x) = g(x)$ almost everywhere.
• $\int_a^b f(x)dx \ge \int_a^b g(x)dx$ is the correct integral comparison inequality.
• The inequality is reversed.
• Integrals exist since the problem states $f$ and $g$ are integrable.