pure maths integration

Consider f'(x) = e^(x^2) - 1

For f to be strictly increasing, check for f'(x) >= 0:

e^(x^2) - 1 >= 0

e^(x^2) >= 1

x^2 >= 0

Also since f'(x) = 0 only when x = 0, that is, x = 0 is a resting point but not a rangeof flat curve, so conclusively we can say that:

f(x) is strictly increasing for all real values of x.