Determine the value of the positive integer constant A that satisfies this relationship:

6
∫ {y}^[y] dy = 19/20
A

Bonus Question:

What are the possible pair(s) of the positive integer constants (B, C) that satisfy this relationship?

C
∫ [y]^{y} * ln [y] dy = 18
B

Notes:

(i) [x] is the greatest integer ≤ x, and {x}= x - [x]

(ii) ln x is the natural logarithm of x.