Bounded variables

Can someone tell me why the variables are bounded in these instances?

1. i in Σ_i=a ⁿ f(i)
2. x in ∫_a^b f(x) dx

>>2
Could you explain how they are within a "for all" or "there exists" statement? Bounded variables are bounded only if they are within such things. I do not see any "for all" or "there exists."