  Rough paths techniques give the ability to define solutions of stochastic
differential equations driven by signals $X$ which are not semimartingales and
whose $p$-variation is finite only for large values of $p$. In this context,
rough integrals are usually Riemann-Stieltjes integrals with correction terms
that are sometimes seen as unnatural. As opposed to those somewhat artificial
correction terms, our endeavor in this note is to produce a trapezoid rule for
rough integrals driven by general $d$-dimensional Gaussian processes. Namely we
shall approximate a generic rough integral $\int y \, dX$ by Riemann sums
avoiding the usual higher order correction terms, making the expression easier
to work with and more natural. Our approximations apply to all controlled
processes $y$ and to a wide range of Gaussian processes $X$ including
fractional Brownian motion with a Hurst parameter $H>1/4$. As a corollary of
the trapezoid rule, we also consider the convergence of a midpoint rule for
integrals of the form $\int f(X) dX$.
