$\backslash$table$[[$Definite integrals,$\backslash$table$[[$When we defined the definite integral, ${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx,$ we made two conditions:$],[1.$ The interval over which we integrated, $a,b,$ was a finite interval, and$],[2.$ The function $f(x)$ was continuous on $a,b($ensuring that the range of $f$ was finite$).]]],[,$In the section that follow we consider integrals where one or both of the above conditions do not hold. Such integrals are called improper integrals.$],[$Improper integrals,$\backslash$table$[[$These integrals are not literally "improper," like maybe you shouldn't do them, they're just a little different.$],[$They are integrals$],[-$ for which one or both limits of integration are not strictly defined, or$],[-$ that have a discontinuity somewhere between the limits of integration.$]]],[\backslash$table$[[$Integrals with$],[$infinite$],[$limits$]],\backslash$table$[[$Integrals for which one or both of the limits of integration are not strictly defined are integrals with infinite limits$.$ For example,$],[-{\displaystyle \underset{a}{\overset{}{}}}f(x)dx$