{{{id=2|
def my_range(a, b, N):
    for x in xrange(1, N+1):
        yield (a+(x-1)*(b-a)/N, a+x*(b-a)/N)
///
}}}

{{{id=1|
def curve_approx(f,a,b,N):
    x = var('x')
    s = var('s')
    tmp = var('tmp')
    s = 0
    for x in my_range(a,b,N):
        tmp = 0
        for j in list((i(x[1])-i(x[0]))^2 for i in f):
            tmp = tmp + j
        tmp = sqrt(tmp)
        s = s + tmp
    return s
///
}}}

{{{id=5|
curve_approx((t-1, 3*(t^2)+2, 6*(t^3)-3), 0, 2, 100).n()
///
49.9997944874641
}}}

{{{id=3|
curve_approx((sin(t)^3, cos(t)^3), 0, pi, 100).n()
///
2.99987682724496
}}}

{{{id=7|
2*curve_approx((t, sqrt(1-(t^2))), 0, 1, 100).n()
///
3.14129856716022
}}}