$\int \limits_1^4 \large\frac{2 e^{\Large \sin x^2}}{x}$$=f(k)-f(1)$ then find $k$=? if $\large\frac{d}{dx}$$f(x)=\Large\frac{e^{\sin x }}{\normalsize x}$

Question

\[\begin {array} {1 1} (a)\;k=14 \\ (b)\;k=16 \\ (c)\;k=10 \\ (d)\;k=18 \end {array}\]