Section 5.3 Fundamental Theorem of Calculus Topic 1: Area Functions Definition Area Function Let 𝑓 be a continuous function for 𝑡 ≥ ? . The area function for 𝑓 with left endpoint ? is 𝐴(𝑥) = ∫ 𝑓(𝑡) 𝑑𝑡 𝑥 ? , where 𝑥 ≥ ? . The area function gives the net area of the region bounded by the graph of 𝑓 and the 𝑡 -axis on the interval [?, 𝑥] .