Finding the Vertical Line That Splits a Curve's Area in Two

[epkid08]

Homework Statement

Find the vertical line x = c such that it splits the area under curve f on the interval [a, b], into two equal parts.

Homework Equations

The Attempt at a Solution

I left the specifics out of the problem.

I see two ways to figure this out.

1. Find $$\frac{1}{2}\int^b_af dx$$ and set it equal to $$\int^c_a f dx$$ and solve for c.

2. Set $$\int^c_a f dx$$ equal to $$\int^b_c f dx$$ and solve for c.

Both ways seem like they should give the same answer, but unfortunately they don't. My question is which method is right and why?

 

[Billy Bob]

Both ways give same answer. Recheck your work.