Evaluate Definite Integral Calculus 101: 3x^2 + 4x - 5 from 1 to 2

The problem asks us to evaluate the definite integral:

To evaluate this definite integral, we first find the antiderivative of the integrand .
Using the power rule for integration, which states that (where ), we can find the antiderivative of each term:
The antiderivative of is .
The antiderivative of is .
The antiderivative of is .

So, the antiderivative of is .

Now, we use the Fundamental Theorem of Calculus to evaluate the definite integral. The theorem states that , where is the antiderivative of .

In this case, and .
We need to calculate .

First, evaluate :

Next, evaluate :

Finally, subtract from :

.

The final answer is .