  In this paper we study the integral of the supremum process of standard
Brownian motion. We present an explicit formula for the moments of the integral
(or area) A(T), covered by the process in the time interval [0,T]. The Laplace
transform of A(T) follows as a consequence. The main proof involves a double
Laplace transform of A(T) and is based on excursion theory and local time for
Brownian motion.
