  In this paper, we give evaluations of integrals involving the arctan and the
logarithm functions, and present several new summation identities for odd
harmonic numbers and Milgram constants. These summation identities can be
expressed as finite sums of special constants such as $\pi$, the Catalan
constant, the values of Riemann zeta function at the positive odd numbers and
$\ln2$ etc.. Some examples are detailed to illustrate the theorems.
