Let the function $\mathrm{F}$ be defined as $\text{F}\left(x\right)=\underset{1}{\overset{x}{\int }}\frac{{\text{ e}}^{\text{t}}}{\text{t}}\text{dt}, x>0$, then the value of the integral $\underset{1}{\overset{x}{\int }}\frac{{\text{e}}^{\text{t}}}{\text{t}+\text{a}}\text{dt}$, where $\mathrm{a}>0$, is

• A

  ${\text{e}}^{\text{a}}\left[\text{F}\left(x\right)-\text{F}\left(1+\text{a}\right)\right]$
• B

  ${\text{e}}^{-\text{a}}\left[\text{F}\left(x+\text{a}\right)-\text{F}\left(\text{a}\right)\right]$
• C

  ${\text{e}}^{\text{a}}\left[\text{F}\left(x+\text{a}\right)-\text{F}\left(1+\text{a}\right)\right]$
• Correct answer
  D

  ${\text{e}}^{-\text{a}}\left[\text{F}\left(x+\text{a}\right)-\text{F}\left(1+\text{a}\right)\right]$

Hence, the correct answer is option: 'D'.