Chapter 13 - Section 13.3 - The Definite Integral: Numerical and graphical Viewpoints - Exercises - Page 987: 21

$\dfrac{1}{2} \ sq. units$

We are given that $f(x)=\int_0^1 x \ dx$ Here. the area of a triangle is equal to $A= \int_0^1 (x) \ dx$ $=\dfrac{1}{2} \times (Base) \times Height$ $=\dfrac{1}{2} (1)(1)$ Thus, $\int_0^1 (x) \ dx=\dfrac{1}{2} \ sq. units$