** Final Answer

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** Step-by-step Solution **

Problem to solve:

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Expand the integral $\int\left(x+1\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

Learn how to solve integrals of polynomial functions problems step by step online.

$\int xdx+\int1dx$

Learn how to solve integrals of polynomial functions problems step by step online. Integrate int(x+1)dx. Expand the integral \int\left(x+1\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int xdx results in: \frac{1}{2}x^2. The integral \int1dx results in: x. Gather the results of all integrals.

** Final Answer

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