Math Help - conditional variance of stochastic integral

1. conditional variance of stochastic integral

Hallo!
I've problems to compute the conditional variance of a Brownian Integral.

I've written my problem in an extra file in the attachment.

I appreciate any help.
$var(\int\limits_0^Tf(u)dB_u|\mathcal{F}_t)=\int\li mits_t^Tf^2(u)du.$