- Example: f′(x) = x + 1, find f(1) by summing from 0 (continued from last time)
- Riemann sums
- Sum of function values in x sub-intervals times sub-interval widths
- Sub-interval widths and x value selected for each interval can vary
- If all Riemann sums over interval [a,b] have same limit as
sub-interval width goes to 0, that limit is the definite integral
of f(x) over [a,b]
- Some properties of definite integrals
- The fundamental theorem of calculus
- Read Section 5.4