Exercises from [Foll13]:
Chapter 1: Exercises 3 (with the sets in 3(a) nonempty), 7, 10, 12, 14; 15, 17, 18, 19, 22(a), 24, 28; 26, 30, and 31.
Chapter 2: Exercises 2, 3, 7, 9 (in 9(c), Exercise 1.29 may be used without proof); 10, 12, 13, 14, 16, 19; 24, 25, 28(a,b), 33, 34, 35, 38, 41; 40, 44, 47, 49, 50, 51, 52, 54, 56, 58, 59. Exercise 24 shows that upper sums are not needed in the definition of the integral.
Chapter 3: Exercises 3(b,c), 5, 6, 9, 12, 13, 14, 16, 20, 21, 22.
[Foll13]
Folland, G. B., Real analysis:
Modern techniques and Their applications,
John Wiley & Sons, Incorporated, Wiley, 2013