$$\begin{aligned} &\int_0^{\mathrm{x}} \mathrm{tf}(\mathrm{t}) \mathrm{dt}=\mathrm{x}^2+(\mathrm{x}), \mathrm{x}>0\\ &\text { Diff. both side w.r. to } x\\ &\begin{aligned} & x f(x)=x^2 f^{\prime}(x)+2 x f(x) \\ & -x f(x)=x^2 f^{\prime}(x) \\ & \int \frac{f^{\prime}(x)}{f(x)} d x=\int \frac{-1}{x} d x \\ & \operatorname{logdf}(x)=-\log x+\log c \\ & f(x)=\frac{c}{x} \end{aligned}\\ &\mathrm{f}(2)=3 \Rightarrow 3=\frac{\mathrm{c}}{2} \Rightarrow \mathrm{c}=6\\ &f(x)=\frac{6}{x}\\ &f(6)=1\quad\therefore (1) \end{aligned}$$