Let's do it with respect to y, It'll be easier.

Recall that

when we want to find area between curves with respect to y.

Step 1. Find limits of integration.

We need to know over what interval y will move along. This is easy. From the context of the question (i.e find the are between curves from y=0 to y=1).

So, we see that

and

.

Step 2 Determine which is the

and which is the

.

If we were to draw a line which is parallel to the x-axis we would see that the curve

would intersct this line to the left of where

would intersect said line. Therefore

and

.

Step 3. Get every thing in terms of y

And

Step 4. Substitute the relevant information into the formula

Step 5. Evaluate

If you need help with step 5, let me know.