Definition: The definite integral is ₐ∫ᵇ f(x) dx = _(n → ∞ )lim [ ᵢ₌₁Σⁿ f(cᵢ) • ∆x ]

if the lim exists & if the width of all subintervals approaches 0 as n → ∞, f is then called Integratable on [a,b]