The area of the region bounded by the curve $y = f(x)$, the $x$-axis and the ordinates $x = a$ and $x = b$ (with $b > a$) is given by which expression?

1. An elementary vertical strip has height $y = f(x)$ and width $dx$, so its area is $dA = y\,dx$. 2. Summing strips from $x = a$ to $x = b$ gives $A = \int_a^b y\,dx = \int_a^b f(x)\,dx$. 3. We integrate the function itself, not its derivative, so the area is $\int_a^b f(x)\,dx$. _Source: NCERT Class 12 Mathematics Ch 8 "Application of Integrals", p.2_