Compact interval/Riemann integrable/Definite integral/Definition
Definite integral
Let denote a compact interval. For a Riemann-integrable function
![{\displaystyle {}I=[a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d9415455379ef65b8bcc5629a5e182b7e8909e52)
![{\displaystyle f\colon I=[a,b]\longrightarrow \mathbb {R} ,t\longmapsto f(t),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/779ff7e82bd2fe21d83e7fc23e46e84d1e970300)
we call the upper integral of (which by definition coincides with the lower integral) the definite integral of over . It is denoted by
