Help with curves please!

Question

Which of the following integrals represents the area of the region bounded in the first quadrant by x =  and the functions f(x) = sec²(x) and g(x) = sin(x)?

Options:

1)
2)
3)
4)

Answer 1

Answer is 2): Area S = = (tanx + cosx) with substitution from x = 0 to x = π/4.

S = (tanπ/4 + cosπ/4) - (tan0 + cos0) = 1 + 1/2^1/2 - 0 - 1 = sqrt2/2