Hàm số liên tục trên $\mathbb{R}$
$\Rightarrow \displaystyle\lim_{x \to 0^-} f(x)= \displaystyle\lim_{x \to 0^+} f(x)\\ \Leftrightarrow \displaystyle\lim_{x \to 0^-} 2x\sqrt{3+x^2}= \displaystyle\lim_{x \to 0^+} (e^x+m)\\ \Leftrightarrow 0=1+m\\ \Leftrightarrow m=-1\\ I=\displaystyle\int\limits^1_{-1} f(x) \, dx\\ =\displaystyle\int\limits^0_{-1} f(x) \, dx+\displaystyle\int\limits^1_{0} f(x) \, dx\\ =\displaystyle\int\limits^0_{-1} 2x\sqrt{3+x^2} \, dx+\displaystyle\int\limits^1_{0} (e^x-1) \, dx\\ =\displaystyle\int\limits^0_{-1} \sqrt{3+x^2} \, d(x^2+3)+\displaystyle\int\limits^1_{0} (e^x-1) \, dx\\ =\dfrac{2}{3}\sqrt{(3+x^2)^3}\Bigg\vert^0_{-1}+(e^x-x)\Bigg\vert^1_{0}\\ =2\sqrt{3}-\dfrac{16}{3}+e-2\\ =2\sqrt{3}-\dfrac{22}{3}+e$
