Compact interval/Riemann integrable/Definite integral/Definition

Definite integral

Let ${}I=[a,b]$ denote a compact interval. For a Riemann-integrable function

Failed to parse (syntax error): {\displaystyle f \colon I <table class="metadata plainlinks ambox ambox-notice" style=""> <tr> <td class="mbox-image"><div style="width: 52px;"> [[File:Wikiversity logo 2017.svg|50px|link=]]</div></td> <td class="mbox-text" style=""> '''[[m:Soft redirect|Soft redirect]]'''<br />This page can be found at <span id="SoftRedirect">[[mw:Help:Magic words#Other]]</span>. </td> </tr> </table>[[Category:Wikiversity soft redirects|Compact interval/Riemann integrable/Definite integral/Definition]] __NOINDEX__ [a,b] \longrightarrow \R , t \longmapsto f(t) , }

we call the upper integral of ${}f$ (which by definition coincides with the lower integral) the definite integral of ${}f$ over ${}I$. It is denoted by

$\int _{a}^{b}f(t)\,dt{\text{ or by }}\int _{I}^{}f(t)\,dt.$