What Is an Integral Function? - Expii

The simplest kind of integral function, which is relevant to FTC, is \(F(x) = \int_a^x f(t)\,dt\), where \(f\) is a function and \(a\) is a constant (so only the upper endpoint, \(x\), varies). Note that when you plug in a value of \(x\) less than \(a\), you get a backwards definite integral. Later on, we'll also look at more complicated integral functions.