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We consider integrals $\tau_{\rho}=\int_0^1\rho\xi^2\,dx$, where $\xi$ isWiener process and $\rho$ is generalized function from some class ofmultipliers. In the case when multiplier $\rho$ belongs to the trace-class, itis shown that $\tau_{\rho}$ has $\chi^2$-distribution (or analogous). Anexample of multiplier $\rho$ not belonging to the trace-class is constructed.

Some remarks on integral parameters of Wiener process