Covariance of integrated Brownian bridge

Question

How to find the Covariance of $Z(p)$ and $Z(q)$, where $$Z(p)=\int_0^p B(u)du+\int_p^1 \frac{B(u)}{1-u}du$$ and $B(u)$ is the standard Brownian Bridge on $[0,1]$. My approach is that $Z(p)=\int_0^p B(u)du+\int_p^1 \frac{B(u)}{1-u}du$ is a Gaussian process with mean $0$. To find the covariance, I proceed as \begin{eqnarray*} Cov(Z(p),Z(q))&=&\int_0^p\int_0^q E[B(u)B(v)]dv du+\int_0^p\int_q^1\frac{E[B(u)B(v)]}{1-u} dv du\\ &+&\int_p^1\int_0^q\frac{E[B(u)B(v)]}{1-u} dv du +\int_p^1\int_q^1\frac{E[B(u)B(v)]}{(1-u)^2} dv du\\ &=& \int_0^p\int_0^q [min\{u,v\}-uv]dv du+ \int_0^p\int_q^1\frac{[min\{u,v\}-uv]}{1-u} dv du\\&+& \int_p^1\int_0^q\frac{[min\{u,v\}-uv]}{1-u} dv du +\int_p^1\int_q^1\frac{[min\{u,v\}-uv]}{(1-u)^2} dv du. \end{eqnarray*}