(a) Prove that I=∫ −[infinity]
[infinity]
​
x 4
+4
dx
​
= 4
π
​
. [10] Notice that this is an improper integral. (b) Let the f(z) be analytic function defined on a bounded domain D and continuous on D and its boundary ∂D. Suppose that f(z) is not a constant function. Prove that if ∣f(z)∣= 2
​
∈R on ∂D, then f(z) must have at least one zero in D. [10]