What is the correct formula for Parseval's identity?

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Looking for a quick validation here:

We have a periodic function $f(t)$ with a period of $T$ that satisfies Dirichlet's conditions. Which of the following 2 formulas is correct ?

My book (not professor's):

$$\int_{-T/2}^{T/2}f(t)^2dt = \frac{a_0^2}{4} + \frac{1}{2}*\sum_{n=1}^{\infty}(a_n^2+b_n^2)$$

My professor's slides:

$$\int_{-T/2}^{T/2}f(t)^2dt = {a_0^2} + \frac{1}{2}*\sum_{n=1}^{\infty}(a_n^2+b_n^2)$$

Which of these 2 is the correct one?