\( \int _{}^{}(2x-1) d \)

To evaluate the integral \( \int (2x - 1) \, dx \), think of it as gathering the treasure of antiderivatives! The integral of \( 2x \) is \( x^2 \) (because when you differentiate \( x^2 \), you get \( 2x \)), and the integral of \( -1 \) is \( -x \). Don’t forget to add the constant of integration, \( C \), since there are infinitely many antiderivatives differing by a constant. Therefore, the answer is: \[ x^2 - x + C \] This little gem can help you find areas under curves or solve differential equations! When you encounter an expression to integrate, a common mistake is to forget the \( dx \) at the end. It’s like forgetting the cherry on top of a sundae! Always ensure that your integral notation is complete to avoid confusion. Sometimes people also mistake constants for variables, leading to incorrect antiderivatives. Keep those basics in check, and you’ll breeze through your integrations!