A series representation for Riemann's zeta function and some interesting identities that follow

Using Cauchy's Integral Theorem as a basis, what may be new series representation for Dirichlet's function $\eta(s)$, and hence Riemann's $\zeta(s)$, is obtained in terms of the Exponential $E_{s}(i\kappa)$ complex argument. From this infinite sums are evaluated, unusual integrals reduced to known functions interesting identities unearthed. The incomplete $\zeta^{\pm}(s)$ $\eta^{\pm}(s)$ defined shown intimately related some these integrals. An identity relating Euler, Bernouli Harmonic numbers developed. It demonstrated that simple integral with endpoints can utilized evaluate large number different integrals, by choosing varying paths between endpoints.