It is shown that for any quasi integral \(I\) on a Stone lattice \(L\) with \(I(1)= 1\) there exists a unique upper-continuous capacity \(\mu\) on the collection \(\Sigma\) of all upper contours of all functions belonging to \(L\) satisfying \(I(a)= \int_X ad\mu\), \(a\in L\). Moreover, \(I\) introduced by \(I(a)= \int_X ad\mu\), \(a\in L\), for some upper-continuous capacity \(\mu\) on \(\Sigma\) is a quasi integral on \(L\). Here \(\int_X ad\mu\) is defined as the Choquet integral \[ \int^\infty_0 \mu(a\geq t)dt+ \int^0_{-\infty} (\mu(a\geq t)- 1)dt,\quad a\in L. \] As an application it is shown that the set consisting of all upper continuous capacities on a compact space equipped with the weak topology is a compact Hausdorff space, which is in addition metrizable, if the underlying compact space is metrizable.