  The global behaviour of the normal function associated with van Geemen's
family of lines on the mirror quintic is studied. Based on the associated
inhomogeneous Picard-Fuchs equation, the series expansions around large complex
structure, conifold, and around the open string discriminant are obtained. The
monodromies are explicitly calculated from this data and checked to be
integral. The limiting value of the normal function at large complex structure
is an irrational number expressible in terms of the di-logarithm.
