Đáp án:
$A$
Giải thích các bước giải:
$I=\displaystyle\int\limits^m_0 f(x) \, dx\\ m-t=x\\ -dt=dx\\ \begin{array}{|c|c|c|}\hline x&0&m\\\hline t&m&0\\\hline\end{array}\\ I=-\displaystyle\int\limits^0_m f(m-t) \, dt\\ =\displaystyle\int\limits^m_0 f(m-x) \, dx\\ I'=\displaystyle\int\limits^m_0 \left(x.f'(m-x)-f(x)\right) \, dx\\ =\displaystyle\int\limits^m_0 \left(x.f'(m-x)-f(m-x)\right) \, dx\\ =-\displaystyle\int\limits^m_0 \left(f(m-x)-x.f'(m-x)\right) \, dx\\ =-\displaystyle\int\limits^m_0 \left(xf(m-x)\right)' \, dx\\ =-xf(m-x) \Bigg\vert^m_0\\ =-mf(0)\\ =1\\ f(0)=2021\\ \Rightarrow m=-\dfrac{1}{2021}\\ \Rightarrow a=1,b=2021, a+b=2022\\ \Rightarrow A$
