In this activity, students will build on their comprehension of functions defined by a definite integral, where the independent variable is an upper limit of integration. Students are led to the brink of a discovery of a discovery of the Fundamental Theorem of Calculus.

In this activity, students will explore approximating the area under a curve using left endpoint, right endpoint, and midpoint Riemann sums.

In this activity, students examine functions defined by a definite integral. They create tables and graphs for integration functions. They understand the foundation of the Fundamental Theorem of Calculus.

In this activity, students calculate Riemann sums. They demonstrate when the Riemann sums will over-approximate a definite integral. They also observe the convergence of Riemann sums as the number of subintervals get larger.

In this activity, students explore the connection between an accumulation function, one defined by a definite integral, and the integrand. They also discover that the derivative of the accumulator is the integrand.