Let function F be defined as $\;F(x) =\int \limits_{1}^{x} \large\frac{e^{t}}{t} dt\;$ , x > 0 then the value of the integral $\;\int \limits_{1}^{x} \large\frac{e^{t}}{t+a} dt\;$ , where a > 0 , is :

Question

$(a)\;e^{a} [F(x) -F(1+a)]\qquad(b)\;e^{-a} [F(x+a) -F(a)]\qquad(c)\;e^{a} [F(x+a) -F(1+a)]\qquad(d)\;e^{-a} [F(x+a) -F(1+a)]$