Consider two functions f and g on [2, 7] such that integral^2 to 7 f(x) dx = 10, integral^2_7 g(x) dx = 7, integral^4_7 f(x) dx = 5, and integral^2_4 g (x) dx = 3. Evaluate the following integrals.
a. integral^5_1 2f(x) dx =
b. integral^8_1 (f(x) - g (x)) dx =
c. integral^5_1 (f (x) - g (x)) dx =
d. integral^8_5 (g(x) - f(x)) dx =
e. integral^8_5 7g(x) dx =
f. integral^1_5 3f(x).