Find r(t) if r'(t) = t⁴i + eᵗj + 2te²ᵗk, and r(0) = i + j + k. r(t).

a) t⁵i + (eᵗ - 1)j + (t²e²ᵗ + 1)k
b) t⁴i + (eᵗ + 1)j + (t²e²ᵗ - 1)k
c) t⁵i + (eᵗ + 1)j + (t²e²ᵗ + 1)k
d) t⁴i + (eᵗ - 1)j + (t²e²ᵗ - 1)k