Is there a difference between these formulas and their outcomes? total income = 0 k f(t)dt total income = 0 k f(t)dt total

Is there a difference between these formulas and their outcomes?

total income = ₀ὸ^k f(t)dt

total income = ₀⌡^k f(t)dt

total income = ₀ὑ^k f(t)dt

The question has to do with continuous income streams. It uses the first one formula.

f(t) is annual flow from the income source.

k=years

f(t) = 225e^-0.35t

Need to find total income over next ten years with the given formula, total income = ₀ὸ^k f(t)dt