Eigenvalues of some distal functions

In this paper we construct distal functions of another type discussed by Salehi (1991). Let $a(t)$ be an almost periodic function with the mean value 0, which has unbounded integral, and $\Phi$ a continuous periodic function with the prime period 1. If $\Phi$ satisfies some additional condition, then $f(t)=\Phi(\int^t_0a(s)\,ds)$ is a distal function, which is not almost periodic, and the set of eigenvalues of $f$ is the module of $a$.