Chapter 13 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Section 13.5 The Area Problem; The Integral - 13.5 Assess Your Understanding - Page 923: 5

$$3$$

Our aim is to calculate the approximation of $A$, the area under the function using the left endpoints. We are given that the length of each sub-interval is $1$. Therefore we have: $$A=(2-1)f(1)+(3-2)f(2) \\=f(1)+f(2 )\\=1+2 \\ =3$$