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Integrate a matrix-function


I'm using Mathematical 4.0. The problem is the following.

I have a function, say f[s_,t_], there s,t are real numbers and the output
is a matrix of size (n,n). I need to integrate each component in the matrix,
i.e. make a new function, like this:
g[s_,t_] := Integrate[f[u,t], {u,s,t}] // error

So right now I have a line for each element but I think there is a one-line
way of doing this (using Map or Apply) ?

Thanks IA for any help

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