Find the area between the curve $y=x^2-5x$ and the $x$-axis for $x$ between 0 and 6.
I'm having trouble with this because part of the function (x from 5 to 6) is above the $x$-axis while the other part (0 to 5) is below it... The answer and the steps you take to find it would be insanely helpful! Thanks!
The question is a little ambiguous, most of the time area under a function is used to describe integration. I'll assume that in the first part of this response.
You don't need to worry about what parts of the function are above or below the $x$-axis, it all comes out in the math (your answer will just be negative, which makes perfect sense mathematically).
$$\text{Area} = \int_{0}^6 y(x) dx = \int_0^6(x^2-5x)dx=\int_0^6x^2dx-5\int_0^6xdx$$
I'll leave the rest up to you.
To verify your answer, see https://www.wolframalpha.com/input/?i=integrate+x%5E2-5x+from+0+to+6.
In the case where they are asking for a positive value, that is if you were to shade the region and wish to determine the area of that, you would need to look at your function and determine where it is positive. In the regions where it is negative, multiply by $-1$. In that case, your area is
$$\text{Area} = -\int_0^5(x^2-5x)dx + \int_5^6(x^2-5x)dx$$