The Additivity Theorem
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Let be a real-valued function on the interval , and let . Then, is Riemann integrable on if and only if it is also Riemann integrable on and . In this case, we have that
![{\displaystyle [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4b788fc5c637e26ee98b45f89a5c08c85f7935)
![{\displaystyle [a,c]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/70b45aa26fb924cdd37786af1adcf5d58cfe15af)
![{\displaystyle [c,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/07f3f774df12e18b9f2bb94333ff320bbd2c308d)
