Find f. (antiderivative) . f '(t) = 4 cos (t) + sec^2(t), −π/2 < t < π/2, f(π/3) = 3

The antiderivative of the function f '(t) = 4 cos (t) + sec^2(t) is determined by applying integral calculus. The antiderivative of 4 cos (t) is -4 sin(t) while the antiderivative of sec^2(t) is tan (t). The total term is -4 sin(t) + tan (t). We try to replace pi/3 and the answer is 3.