quantum mechanics - Dyson series derivation

$$ i\hbar \frac{dU_I(t, t_i)}{dt} = \hat{V}_I(t)\hat{U}_I(t,t_i) \tag{10.32} $$ The solutions of this equation, with the initial condition $\hat{U}_I(t_i,t_i)$, are given by the integral equation $$ \hat{U}_I(t,t_i) = 1 - \frac{i}{\hbar}\int_{t_i}^t\hat{V}_I(t')\hat{U}_I(t',t_i)dt' \tag{10.33} $$

In the derivation of Dyson Series please explain why in equation (10.33) $t$ is changed to $t'$ without integrating.