(a) Determine the equation of the tangent line to $y=x^2$ at the point (1, 1).

Tangent line: $y =$

(b) Find the area of the region bounded by the parabola $y=x^2,$ the tangent line to this parabola at (1, 1) that you found in (a), and the $x$-axis.

Area =

You can earn partial credit on this problem.