Let $I$ be an interval in the sense of \ref{def:interval-real-line-c54-2026a}, let $[a,b]\subseteq I$, let $f:I\to\mathbb{R}$ be continuous on $[a,b]$ in the sense of \ref{def:continuity-closed-interval-c54-2026a}, and let $F:I\to\mathbb{R}$ be an antiderivative of $f$ on $I$ in the sense of \ref{def:antiderivative-interval-c54-2026a}. Then $\int_a^b f(x)\,dx = F(b)-F(a),$ where the integral is the Riemann integral of \ref{def:riemann-integrable-closed-interval-c54-2026a}.