I'm stuck on this problem and any help would be appreciated.

"A metal plate, with constant density 2 g/cm^2, has a shape bounded by the curve y=x^2 and the x-axis, with 0 less than or equal to x, which is less than or equal to 1 and x,y in cm.

a) Find the total mass of the plate."

I know that if the density's given like that, you can multiply it by the length and get the mass, but I don't know how to find the length with the information given.

I also know you can take the integral of the density function to get the same thing, but since the numerical value of the density's already given, I figured it was the first method that was right.

Help, please?