1. The problem is to understand integration sums, which are methods to approximate the area under a curve using sums. 2. The main types of integration sums are Left Riemann Sum, Right Riemann Sum, and Midpoint Riemann Sum. 3. For a function $f(x)$ on interval $[a,b]$, divide the interval into $n$ equal parts of width $\Delta x = \frac{b-a}{n}$. 4. Left Riemann Sum uses the left endpoints: $$L_n = \sum_{i=0}^{n-1} f(a + i\Delta x) \Delta x$$ 5. Right Riemann Sum uses the right endpoints: $$R_n = \sum_{i=1}^n f(a + i\Delta x) \Delta x$$ 6. Midpoint Riemann Sum uses midpoints: $$M_n = \sum_{i=0}^{n-1} f\left(a + \left(i + \frac{1}{2}\right)\Delta x\right) \Delta x$$ 7. These sums approximate the definite integral $$\int_a^b f(x) \, dx$$ and become more accurate as $n$ increases. 8. Integration sums are foundational for understanding definite integrals and the Fundamental Theorem of Calculus.