Hi Rahul,

Let's try this with $n = 3.$ The sum is then

\[ \sum_{k=1}^{k=3} x^k\]

which unpacks to

\[x^1 + x^2 + x^{3}.\]

Thus you have

\[\int_{0}^{b} {1 + x^1 + x^2 + x^3} dx.\]

Evaluate this definite integral and rewrite the answer using summation notation. Can you make it look like the answer given in your question with $n = 3?$

This works because the integral of a sum is the sum of integrals. That is

\[\int_{0}^{b} {1 + x^1 + x^2 + x^3} dx = \int_{0}^{b}{1}\; dx+ \sum_{k=1}^{k=3} {\int_{0}^{b} {x^k}}{dx}. \]

Try to repeat this with $k = 1$ to $k = n.$

Write back if you need more assistance,
Penny