Given a set P of n points on the real line and
a(potentially infinite) family of functions, we investigate the
problem of finding a small(weighted) subset \Coreset \subseteq
P, such that for any f in \Family, we have that f(P)
is a (1\pm µ)-approximation to f(\Coreset).
Here, f(Q)=\sum_{q in Q} w(q) f(q) denotes
the weighted discrete integral of f over the point set
Q, where w(q) is the weight assigned to the
point q.

We study this problem, and provide tight
bounds on the size \Coreset for several families of functions.
As an application, we present some coreset constructions for
clustering.