  In this article we study properties of Ramanujan's mock theta functions that
can be expressed in Lerch sums. We mainly show that each Lerch sum is actually
the integral of a Jacobian theta function (here we show that for
$\vartheta_3(t,q)$ and $\vartheta_4(t,q)$) and the $\sec-$function. We also
prove some modular relations and evaluate the Fourier coefficients of a class
of Lerch sums.
