Solve $\int_{0}^{1} (2 x + 1) d x$

Step-by-step solution

Step 1 · Power rule for integration
$\int (2 x + 1) d x = x^{2} + x + C$
Integrate each term separately.
Step 2 · Fundamental theorem of calculus
$[x^{2} + x]_{0}^{1}$
A definite integral equals the change in any antiderivative.
Step 3 · Evaluate
$(1 + 1) - (0 + 0) = 2$
The area under the line between 0 and 1 is 2 square units.

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