# Who's up to the challenge? 47

Calculus Level 4

$\large \int_0^{2016} H_x^{(2)} \, dx$

Let $${ H }_{ n }^{ (2) }$$ be the generalized harmonic number of order $$n$$ of 2, $$\displaystyle H_n ^{(2)} = \sum_{k=1}^n \dfrac 1{k^2}$$.

If the integral above is equal to $$a\zeta(b) - H_c$$, where $$a,b$$ and $$c$$ are positive integers, find $$a+b+c$$.

Notations:

×