1. Prove that
if f(x) and g(x) are functions which are integrable on [a,b].
2. Consider the polynomial h(x) = x2 - x + 41. Note that h(1) = 41, h(2) = 43, h(3) = 47, h(4) = 53, and h(5) = 61 are all prime numbers. Is h(x) always a prime number if x is a positive integer? Why or why not?
Solution. h(41) = 412 - 41 + 41 = 412.
Bonus. Is there any (other?) polynomial which always gives you prime numbers?