Notice that

So 10 out of your 100 terms give f(1)

and

5 of these terms give f(0.5) and 5 more give f(2).

Already, we have regrouped 20 out of 100 of these terms in 3 simple operations: 10f(1)+5f(0.5)+5f(2).

I suspect the 80 remaining could also be regrouped like this!