Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a continuous function satisfying
$f(x)=e^{x^2 / 2}+\int_0^x t f(t) d t \quad \text { for all } x$
Then which of the following is correct?

• A

  $2 \lt f(\sqrt{2}) \lt 3$
• Correct answer
  B

  $5 \lt f(\sqrt{2}) \lt 6$
• C

  $4 \lt f(\sqrt{2}) \lt 5$
• D

  $3 \lt f(\sqrt{2}) \lt 4$

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