Clear[f]
f[x_] := x^2
a = 1; b = 2
Plot[f[x], {x, a, b}, AxesOrigin -> {0, 0}]
Clar[t]
x = a + t (b - a)/Pi

Clar[t]

Clear[h]
h[t_] = f[x]
Plot[h[t], {t, 0, Pi}, AxesOrigin -> {0, 0}]