Recall the function f(x) that we worked with in Riemann Sums and Trapezoid Rule.
When applying Riemann Sums (utilizing rectangles)...

...and the Trapezoid Rule (utilizing trapezoids)...

...we were estimating the integral with shapes (rectangles and trapezoids).
What if we wanted to calculate the exact integral?

Herein lies the purpose of definite integrals...