THIS theorem: Let $I =[a,b]$ be a closed and bounded interval and $\forall n\in \mathbb{N}$, $f_n:I \to \mathbb{R}$ be Riemann integrable on $I$. If the sequence $(f_n)$ converges uniformly to a function $f$ on $I$ then $f$ is $R$ integrable on $I$ and moreover, the sequence $\int_a^bf_n$ converges to $\int_a^bf$.
Now, the restrictions imposed on DCT is far less than the previously mentioned theorem. First of all (rather based on intuition), $Riemann \implies Lebesgue$, but not the other way around. $uniformly \ convergent \implies pointwise \ convergent$. Again, every compact set in $\mathbb{R}$ Lebesgue measureable.
So, in my view, $THIS \ Theorem \implies DCT$, but not always the other way around.
Is my thinking valid?