Calculus Antiderivative?

a(t) = t² - 7t + 6

v(t) = ∫(t² - 7t + 6) dt
v(t) = (1/3)t³ - (7/2)t² + 6t + C₁

s(t) = ∫(1/3)t³ - (7/2)t² + 6t + C₁
s(t) = (1/12)t⁴ - (7/6)t³ + 3t² + C₁t + C₂

S(0) = 0 :
(1/12)(0)⁴ - (7/6)(0)³ + 3(0)² + C₁(0) + C₂ = 0
C₂ = 0
Hence, s(t) = (1/12)t⁴ - (7/6)t³ + 3t² + C₁t

S(1) = 20
(1/12)(1)⁴ - (7/6)(1)³ + 3(1)² + C₁(1) = 20
(1/12) - (7/6) + 3 + C₁ = 20
C₁ = 20 - (1/12) + (7/6) - 3
Hence, C₁ = 217/12

The position of the particle :
s(t) = (1/12)t⁴ - (7/6)t³ + 3t² + (217/12)t