Riemann Sum Notation - Pugh

What is the lower limit?

$$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{7}{n}\right)\left[4\left(-4+\frac{7k}{n}\right)+2\right]$$

What is the upper limit?

$$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{2}{n}\right)\left[3\left(-1+\frac{2k}{n}\right)-\left(-1+\frac{2k}{n}\right)^3\right]$$

What is the upper limit?

$$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{-6}{n}\right)\left[\left(3-\frac{6k}{n}\right)^2-5\left(3-\frac{6k}{n}\right)+2\right]$$

Select the correct integral notation for the summation below:

$$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{3}{n}\right)\left[\left(\frac{3k}{n}\right)^3\right]$$

Select the correct integral notation for the summation below:

$$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{5}{n}\right)\left[1-5\left(-2+\frac{5k}{n}\right)^2\right]$$

Select the correct integral notation for the summation below:

$$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{\pi}{n}\right)\left[\cos\left(\pi+\frac{\pi k}{n}\right)\right]$$

Select the correct integral notation for the summation below:

$$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{5}{n}\right)\left[4\left(\frac{5k}{n}\right)\right]$$

Select the correct integral notation for the summation below:

$$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{2}{n}\right)\left[2\left(4+\frac{2k}{n}\right)^2\right]$$

Select the correct integral notation for the summation below:

$$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{4}{n}\right)\left[\left(-5+\frac{4k}{n}\right)^2+3\left(-5+\frac{4k}{n}\right)+5\right]$$

How many rectangles are needed to find the exact area underneath a curve?